SimpleInterest Compound Interest Kinindia.com

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SIMPLE INTEREST

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MODULE OBJECTIVE

Interest

Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of theamount borrowed per period of time, usually one year.

Simple Interest

Simple interest is calculated on the original principal only. Accumulated interest from priorperiods is not used in calculations for the following periods. Simple interest is normally used fora single period of less than a year, such as 30 or 60 days.

Simple Interest = (P *R*T)/100

where:P = principal (original amount borrowed or loaned)R= interest rate for one periodT = number of periods

IMPORTANT FORMULA

Principal:

The money borrowed or lent out for a certain period is called the principal or the sum.

Interest:

Extra money paid for using other's money is called interest.

Simple Interest (S.I.):

If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simpleinterest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

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(i). Simple Intereest =P x R x T

100

SOLVED EXAMPLES

1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4years. The sum is:A.Rs. 650 B.Rs. 690C.Rs. 698 D.Rs. 700

Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and Bat the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount ofsimple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?A.Rs. 6400 B.Rs. 6500C.Rs. 7200 D.Rs. 7500E.None of these

(ii). P =100 x S.I.

; R =100 x S.I.

and T =100 x S.I.

.R x T P x T P x R

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Answer: Option A

Explanation:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).

Then,x x 14 x 2

+(13900 - x) x 11 x 2

= 3508100 100

28x - 22x = 350800 - (13900 x 22)

6x = 45000

x = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years.What is the sum?A.Rs. 4462.50 B.Rs. 8032.50C.Rs. 8900 D.Rs. 8925E.None of these

Answer: Option D

Explanation:

Principal= Rs.100 x 4016.25

9 x 5

= Rs.401625

45= Rs. 8925.

4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5%per annum of simple interest?A. 3.5 years B.4 yearsC. 4.5 years D.5 years

Answer: Option B

Explanation:

Time =100 x 81

years= 4 years.

450 x 4.5

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5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate ofinterest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate ofinterest?A. 3.6 B.6C. 18 D.Cannot be determined

Answer: Option B

Explanation:

Let rate = R% and time = R years.

Then,1200 x R x R

= 432100

12R2 = 432

R2 = 36

R = 6.

6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. Whatis the rate of interest?A.3% B.4%C.5% D.6%E.None of these

Answer: Option D

Explanation:

S.I. = Rs. (15500 - 12500) = Rs. 3000.

Rate =100 x 3000

%= 6%

12500 x 4

7. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1year. In order to clear his dues at the end of 2 years, he would pay:A.Rs. 105 B.Rs. 110C.Rs. 115 D.Rs. 115.50

Answer: Option C

Explanation:

Amount to be paid

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= Rs. 115.

8. An automobile financier claims to be lending money at simple interest, but he includesthe interest every six months for calculating the principal. If he is charging an interest of10%, the effective rate of interest becomes:A.10% B.10.25%C.10.5% D.None of these

Answer: Option B

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.100 x 10 x 1

= Rs. 5100 x 2

S.I. for last 6 months = Rs.105 x 10 x 1

= Rs. 5.25100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%

9.A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at thesame rate of interest and received Rs. 2200 in all from both of them as interest. The rate ofinterest per annum is:A.5% B.7%

C.71

%8

D.10%

Answer: Option D

Explanation:

Let the rate be R% p.a.

Then,5000 x R x 2

+3000 x R x 4

= 2200.100 100

100R + 120R = 2200

R =2200

= 10.220

Rate = 10%.

= Rs. 100 +200 x 5 x 1

+100 x 5 x 1

100 100

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10.A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of theyear, Rs. 33.50 is earned as interest from both the loans. What was the original rate ofinterest?A.3.6% B.4.5%C.5% D.6%E.None of these

Answer: Option E

Explanation:

Let the original rate be R%. Then, new rate = (2R)%.

Note:

Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. year(s).

725 x R x 1+

362.50 x 2R x 1= 33.50

100 100 x 3

(2175 + 725) R = 33.50 x 100 x 3

(2175 + 725) R = 10050

(2900)R = 10050

R =10050

= 3.462900

Original rate = 3.46%

11. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years hehad to pay Rs. 5400 interest only for the period. The principal amount borrowed by himwas:A.Rs. 2000 B.Rs. 10,000C.Rs. 15,000 D.Rs. 20,000

Answer: Option C

Explanation:

Principal = Rs.100 x 5400

= Rs. 15000.12 x 3

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12. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at thesame rate of simple interest. The rate of interest per annum is:A.5% B.8%C.12% D.15%

Answer: Option C

Explanation:

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years = Rs.2205

x 5 = Rs. 36753

Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate =100 x 3675

%= 12%

6125 x 5

13. What will be the ratio of simple interest earned by certain amount at the same rate ofinterest for 6 years and that for 9 years?A.1 : 3 B.1 : 4C.2 : 3 D.Data inadequateE.None of these

Answer: Option C

Explanation:

Let the principal be P and rate of interest be R%.

Required ratio =

P x R x 6100

=6PR

=6= 2 : 3.

P x R x 9100

9PR 9

14. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been2% more, how much more interest would it have earned?A.Rs. 35 B.Rs. 245C.Rs. 350 D.Cannot be determinedE.None of these

Answer: Option D

Explanation:

We need to know the S.I., principal and time to find the rate.

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Since the principal is not given, so data is inadequate.

15. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends

it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.A.Rs. 112.50 B.Rs. 125C.Rs. 150 D.Rs. 167.50

Answer: Option A

Explanation:

Gain in 2 years= Rs. 5000 x25

x2

-5000 x 4 x 2

4 100 100= Rs. (625 - 400)= Rs. 225.

Gain in 1 year = Rs.225

= Rs. 112.502

16.A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such thatthey may get equal amounts when each of them reach the age of 21 years. The originalamount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. Howmuch did the elder daughter get at the time of the will?

(A) Rs. 17.5 lakhs (B) Rs. 21 lakhs (C) Rs. 15 lakhs (4D Rs. 20 lakhs

Answer – Option (B)

Solution:

Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the youngerdaughter got (3,500,000 - x).

The elder daughter’s money earns interest for (21 - 16) = 5 years @ 10% p.a simple interestThe younger daughter’s money earns interest for (21 - 8.5) = 12.5 years @ 10% p.a simple interest.

As the sum of money that each of the daughters get when they are 21 is the same,

x + = (3,500,000 - x) +

=> x + = 3,500,000 - x + -

=> 2x + = 3,500,000 (1 + )




Answer: Option A

Explanation:


x2

-5000 x 4 x 2

4 100 100= Rs. (625 - 400)= Rs. 225.


= Rs. 112.502




Solution:




x + = (3,500,000 - x) +

=> x + = 3,500,000 - x + -

=> 2x + = 3,500,000 (1 + )




Answer: Option A

Explanation:


x2

-5000 x 4 x 2

4 100 100= Rs. (625 - 400)= Rs. 225.


= Rs. 112.502




Solution:




x + = (3,500,000 - x) +

=> x + = 3,500,000 - x + -

=> 2x + = 3,500,000 (1 + )

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=> = (3,500,000)=> x = 2,100,000 = 21 lakhs.

DATA SUFFICIENCY PROBLEMS

DIRECTION TO USE

Each of the questions given below consists of a statement and / or a question and two statementsnumbered I and II given below it. You have to decide whether the data provided in thestatement(s) is / are sufficient to answer the given question. Read the both statements and

Give answer (A) if the data in Statement I alone are sufficient to answer the question,while the data in Statement II alone are not sufficient to answer the question.

Give answer (B) if the data in Statement II alone are sufficient to answer the question,while the data in Statement I alone are not sufficient to answer the question.

Give answer (C) if the data either in Statement I or in Statement II alone are sufficient toanswer the question.

Give answer (D) if the data even in both Statements I and II together are not sufficient toanswer the question.

Give answer(E) if the data in both Statements I and II together are necessary to answerthe question.

1. The simple interest on a sum of money is Rs. 50. What is the sum?I. The interest rate is 10% p.a.

II. The sum earned simple interest in 10 years.A.I alone sufficient while II alone not sufficient to answer

B.II alone sufficient while I alone not sufficient to answer

C.Either I or II alone sufficient to answer

D.Both I and II are not sufficient to answer

E.Both I and II are necessary to answer

Answer: Option E

Explanation:

Given : S.I. = Rs. 50.

I gives, R = 10% p.a.

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II gives, T = 10 years.

Sum =100 x S.I.

= Rs.100 x 50

= Rs. 50.T x R 10 x 10

Thus, I and II together give the answer.

2. What is the sum which earned interest?I. The total simple interest was Rs. 7000 after 7 years.

II. The total of sum and simple interest was double of the sum after 5 years.A.I alone sufficient while II alone not sufficient to answer





Answer: Option E

Explanation:

Let the sum be Rs. x.

I gives, S.I. = Rs. 7000 and T = 7 years.

II gives, Sum + S.I. for 5 years = 2 x Sum Sum = S.I. for 5 years.

Now, S.I. for 7 years = Rs. 7000.

S.I. for 1 year = Rs.7000

= Rs. 1000.7

Thus, I and II both are needed to get the answer.

Correct answer is (E).

.

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EXERCISE PROBLEM

. Ex.l Find: S.l. on Rs 68000 at 16 2/3 % per annum for 9 months.

Sol. P = 68000, R = 50/3 % p.a. & T = 9/12 year = 3/4 years.

.. S.I. = ( PxRxT/100)

= Rs. [6800 x 50/3 x ¾ x 1/100] = Rs. 8500

Ex.2 Find: S.l. on Rs 6250 at 14% per annum for 146 days.

Sol.

P = Rs. 6250, R = 14 % p.a. & T = (146/365) year = 2/5 year .

:. S.l. = Rs (6250 x 14 x 2/5 x 1/100)= Rs 350.

Ex.3 Find: S.l. on Rs 3000 at 18% per annum for the period from 4th

Sol.

Time = (24 + 31 + 18) days = 73 days = 1/5 year .

P = Rs 3000 and R = 18 % p.a.

:. S.I. = Rs (3000 x 18 x 1/5 x 1/100)= Rs 108 .

Remark: The day on which money is deposited is not counted while the day on which money iswithdrawn is counted.

Ex. 4. A sum at simple interest at 13 i % per annum amounts to Rs. 2502.50 after 4 years.Find the sum.

Sol. Let sum be x. Then

S.I. = (X x 27/2 x 4 x 1/100) = 27X/50

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.. Amount = ( X + 27X/50) = 77X/50

.. 77X/50 = 2502.50 or X= (2502.50 X 50)/77 = 1625

Hence Sum = Rs.1625

Ex. 5. A certain sum of money amounts to Rs 1008 in 2 years and to Rs 1164 in 3 i years. Findthe sum and (be rate of interest.

Sol.

S.I. for 1 ½ years = Rs (1164 - 1008) = Rs 156 .

S.I. for 2 years = Rs (156 x 2/3 x 2)= Rs 208.

:. Principal = Rs (1008 - 208) = Rs 800.

Now, P = 800, T= 2 and S.I. = 208.

.. Rate = (100 x S.I.) / (P x T) =[ (100x208)/(800x2)]% =13%

Ex.6. At what rate percent per annum will a sum of money double in 8 years

Sol. Let principal = P, Then, S.I.=P and Time=8 years

.. Rate = [(100 x P)/ (P x 8)]% = 12.5% per annum..

Ex. 7. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2%higher rate, it would have fetched Rs 360 more. Find the sum.

Sol. Let, sum = P and original rate = R. Then,

Px (R+2}x 3 P xRx 3 = 360

100 100

or 3PR + 6P - 3PR = 36000 or 6P = 36000 or P = 6000 . Hence, sum = Rs 6000 .

Ex. 8. Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, Ifboth are numerically equal.

Sol. Let sum = x. Then, S.I. = 16x / 25

Let rate = R % and time = R years.

.. ( X x R x R)/(100) = 16x/25 or R2 =1600/25 R= 40/5 =8

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:. Rate = 8% and Time = 8 years.

Ex. 9. A man borrowed Rs 24000 from two money lenders. For one loan, he paid 15% perannum and for the other 18% per annum. At the end of one year, he paid Rs 4050. How muchdid he borrow at each rate ?

Sol. Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).

.. {(X x 15 x 1)/100 + {[(2400 – x) X 18 X 1]/100} = 4050

or 15 x + 432000 - 18x = 405000 or x = 9000.

:. Money borrowed at 15% = Rs 9000 .

Money borrowed at 18% = Rs 15000.

Ex. 10. What annual instalment wiU discharge a debt of Rs 1092 due in 3 years at 12% simpleinterest?

Sol. Let each instalment be Rs. x . then,

{ [x + (X x 12 x 2)/100] + [ X + (X + 12 x 2)/100] + x} =1092

or 28x/25 + 31x/25 +x=1092 or (28x+ 31x+25x) = (1092x25)

or X= {(1092 x 25)/84} = 325

:. Each instalment = Rs. 325

Ex.11 A sum of money invested for a certain number of years at 8% p.a. simple interestgrows to Rs.180. The same sum of money invested for the same number of years at 4% p.a.simple interest grows to Rs.120 only. For how many years was the sum invested?

Solution:From the information provided we know that,

Principal + 8% p.a. interest on principal for n years = 180 …….. (1)

Principal + 4% p.a. interest on principal for n years = 120 ……… (2)

Subtracting equation (2) from equation (1), we get

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4% p.a. interest on principal for n years = Rs.60.

Now, we can substitute this value in equation (2),

i.e Principal + 60 = 120

= Principal = Rs.60.

We know that SI = , where p is the principal, n the number of years and r the rate percent ofinterest.

In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.

Therefore, 60 =

=> n = 100/4 = 25 years.

12. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it isinvested at 12.5% p.a simple interest?

Solution:Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the numberof years for which it is invested, r is the rate of interest per annum

In this case, Rs. 1250 has become Rs.10,000.

Therefore, the interest earned = 10,000 – 1250 = 8750.

8750 = [(1250*n*12.5)/100]

=> n = 700 / 12.5 = 56 years.

DATA SUFFICIENCY PROBLEMS

1. What percentage of simple interest per annum did Anand pay to Deepak?I. Anand borrowed Rs. 8000 from Deepak for four years.

II. Anand returned Rs. 8800 to Deepak at the end of two years and settled the loan.

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A.I alone sufficient while II alone not sufficient to answer





Answer: Option E

Explanation:


I gives, P = Rs. 8000 and T = 4 years.

II gives, S.I. = Rs. (8800 - 8000) = Rs. 800.

R =100 x S.I.

=100 x 800

%= 2

1% p.a.

P x T 8000 x 4 2

Thus, I and II both are needed to get the answer.


2. What is the rate of simple interest?I. The total interest earned was Rs. 4000.

II. The sum was invested for 4 years.A.I alone sufficient while II alone not sufficient to answer





Answer: Option D

Explanation:

We know that, R = 100 x S.I.

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P x T

Now, I gives, S.I. = Rs. 4000.

II gives, T = 4 years.

But, P is unknown. So, we cannot find R.

So, given data is insufficient to get R.

Correct answer is (D).

3. What is the principal sum?I. The sum amounts to Rs. 690 in 3 years at S.I.

II. The sum amounts to Rs. 750 in 5 years at S.I.III. The rate of interest is 5% p.a.

A.I and III only

B.II and III only

C.I and II only

D.I and III only, or II and III only

E. Any two of the three

Answer: Option E

Explanation:

Clearly, any of the three will give us the answer.


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COMPOUNDINTEREST

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COMPOUND INTEREST

Compound interest is calculated each period on the original principal and all interestaccumulated during past periods. Although the interest may be stated as a yearly rate, thecompounding periods can be yearly, semiannually, quarterly, or even continuously.

IMPORTANT FORMULA

Let Principal = P, Rate = R% per annum, Time = n years.

When interest is compound Annually:

Amount = P 1 +R

n100

When interest is compounded Half-yearly:

Amount = P 1 +(R/2)

2n100

When interest is compounded Quarterly:

Amount = P 1 +(R/4)

4n100

When interest is compounded Annually but time is in fraction, say 3 years.

Amount = P 1 +R

3x 1 + R100 100

When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd yearrespectively.

Then, Amount = P 1 +R1 1 +

R2 1 +R3 .

100 100 100

Present worth of Rs. x due n years hence is given by:

Present Worth =x

.1 +

R100

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SOLVED EXAMPLE

1.Find compound interest on Rs. 7500 at 4% per annum for 2 years, compoundedannually.

A. Rs.512 B. Rs.552

C. Rs.612 D. Rs.622

Solution

Amount

= Rs[7500x(1+4/100)²]

=Rs.(7500x26/25x26/25)

= Rs.8112.

C.I= Rs(8112 - 7500)

=Rs.612.

2.Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compoundedquartely.

A. Rs. 2552 B. Rs. 2512

C. Rs. 2572 D. Rs. 2592

Solution

Principal = Rs.16,000;

Time=9 months = 3 quarters;

Amount=Rs.[16000x(1+5/100)³]

=[16000x21/20x21/20x21/20]

= Rs.18522.

C.I= Rs.(18522 - 16000)

= Rs.2522.

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3.Simple interest on a certain sum of money for 3 years at 8% per annum is half thecompound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simpleinterest is

A. Rs. 1550 B. Rs. 1650

C. Rs. 1750 D. Rs. 2000

Solution

C.I. =Rs[4000x(1+10/100)²-4000]

Rs.(4000x11/10x11/10-4000) = Rs.940.

Sum=Rs. [420x100 /3x8]

= Rs.1750.

4.Albert invested an amount of Rs.8000 in a fixed deposit scheme for 2 years atcompound interest rate 5 p.c.p.a. How much amount will Albert get on maturityof the fixed deposit ?

A. Rs. 8600B. Rs.8620

C. Rs. 8840D. Rs.8820

Solution

Amount

=Rs.[8000x(1+5/100)²]

= Rs.[8000 x 21/20x21/20]

= Rs.8820.

5. The present worth of Rs.169 due in 2 years at 4% per annum compound interest is

A. Rs.150.50 B. Rs.154.75

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C. Rs.156.25 D. Rs.158

Solution

Present Worth

= Rs.[169/(1+4/100)²]

= Rs.(169x25/26x25/26)

= Rs.156.25

6.On a sum of money, the simple interest for 2 years is Rs. 660,while the compoundinterest is Rs.696.30,the rate of interest being the same in both the cases. The rate ofinterest is

A. 10% B. 11%

C. 12% D. 10.5%

Solution

Difference in C.I and S.I for 2 years= Rs(696.30-660)

=Rs. 36.30.

S.I for one years = Rs330.

S.I on Rs.330 for 1 year =Rs. 36.30

Rate= (100x36.30/330x1)%

=11%.

7.The difference between simple interest and compound interest on Rs. 1200 for oneyear at 10% per annum reckoned half yearly is

A. Rs.2.50B.Rs.3

C. Rs. 4D.Rs.3.75

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Solution

S.I= Rs.(1200x10x1/100)

Rs.120.

C.I=Rs[(1200x1+5/100)² -1200]

Rs.123.

Difference= Rs.[123-120]

Rs. 3.

8.A sum of money invested at compound interest amounts to Rs. 800 in 3 years and to Rs.840 in 4 years. The rate of interest per annum is

A. 2x1/2% B. 4%

C. 5% D. 6x2/3%

Solution

S.I. on Rs.800 for 1 year=Rs[840 - 800]

= Rs.40

Rate=(100x40/800x1)%

= 5%

9.If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what isthe compound interest on the same at the same rate and for the same time?

A. Rs. 51.25 B. Rs. 52

C. Rs. 54.25 D. Rs. 60

Solution

Sum =Rs.(50 x 100/2x5)

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10.In what time will Rs.1000 become Rs.1331 at 10%per annum compounded annually?

A. 2 years B. 3 years

C. 4 years D. 7 years

Solution

Principal = Rs.1000;

Amount = Rs.1331;

Rate = Rs.10%p.a.

Let the time be n years.Then

[1000(1+10/100)Λn;]

= 1331.

= (1331/1000)

= (11/10)³

Therefore n = 3 years.

= Rs. 500.

Amount

=[Rs.(500x(1+5/100)²]

=Rs(500x21/20x21/20).

=Rs. 551.25

C.I= Rs. (551.25 - 500)

= Rs. 51.25

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11.If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, findthe compound interest on the same sum for the same period at the same rate.

A. 1251 B. 1261

C. 1271 D. 1281

Solution

Clearly, Rate = 5% p.a .,

Time = 3 years

S.I =Rs.1200.

So,Principal=Rs.(100 x 1200/3x5)

=Rs.8000.

Amount

=Rs.[8000 x (1+5/100)³]

=Rs(8000x21/20x21/20x21/20)

= Rs.9261

C.I=Rs.(9261-8000)

=Rs.1261.

12.What will be the compound interest on a sum of Rs.25,000 after 3 years at the rate of 12p.c.p.a?

A. Rs.9000.30 B. Rs. 9720

C. Rs. 10123.20 D. Rs. 10483.20

Solution

Amount

= Rs.(25000x(1+12/100)³

=Rs.(25000x28/25x28/25x28/25)

= Rs. 35123.20.

C.I =Rs(35123.20-25000)

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=Rs.10123.20.

13.The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (inyears) is

A. 2 B. 2½

C. 3 D. 4

Solution

Amount=Rs(30000 + 4347)

= Rs.34347.

Let the time be n years.

Then, 30000(1+7/100)^n

= 34347.

=34347/3000

=11449/1000

=(107/100)^n

n= 2years.

14. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained byway of interest is:

A.Rs. 120 B.Rs. 121

C.Rs. 122 D.Rs. 123

Answer: Option B

Explanation:

Amount= Rs. 1600 x 1 +5

2+ 1600 x 1 +5

2 x 100 2 x 100

= Rs. 1600 x41x41+ 1600 x41

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40 40 40

= Rs. 1600 x41 41

+ 140 40

= Rs.1600 x 41 x 81

40 x 40= Rs. 3321.

C.I. = Rs. (3321 - 3200) = Rs. 121

15. The difference between simple and compound interests compounded annually on a certain sum ofmoney for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

A.625 B.630

C.640 D.650

Answer: Option A

Explanation:

Let the sum be Rs. x. Then,

C.I. = x 1 +4

2- x =676

x- x =51

x.100 625 625

S.I. =x x 4 x 2

=2x

.100 25

51x-2x

= 1625 25

x = 625

16. There is 60% increase in an amount in 6 years at simple interest. What will be the compoundinterest of Rs. 12,000 after 3 years at the same rate?

A.Rs. 2160 B.Rs. 3120

C.Rs. 3972 D.Rs. 6240

E.None of these

Answer: Option C

Explanation:

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Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R =100 x 60

= 10% p.a.100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.= Rs. 12000 x 1 +10

3- 1100

= Rs. 12000 x3311000

= 3972.

17. What is the difference between the compound interests on Rs. 5000 for 1 years at 4% perannum compounded yearly and half-yearly?

A.Rs. 2.04 B.Rs. 3.06

C.Rs. 4.80 D.Rs. 8.30

Answer: Option A

Explanation:

C.I. when interestcompounded yearly

= Rs. 5000 x 1 +4

x 1 + x 4100 100

= Rs. 5000 x26

x51

25 50= Rs. 5304.

C.I. when interest iscompounded half-yearly

= Rs. 5000 x 1 +2

3100

= Rs. 5000 x51

x51

x51

50 50 50= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.04

18. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (inyears) is:

Answer: Option A

Explanation:

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Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be n years.

Then, 30000 1 +7

n= 34347100

107n=

34347=

11449=

1072

100 30000 10000 100

n = 2 years.

19. What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

A.Rs. 9000.30 B.Rs. 9720

C.Rs. 10123.20 D.Rs. 10483.20

E.None of these

Answer: Option C

Explanation:

Amount= Rs. 25000 x 1 +12

3100

= Rs. 25000 x28

x28

x28

25 25 25= Rs. 35123.20

C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20

20. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2years?

A.6% B.6.5%

C.7% D.7.5%

Answer: Option A

Explanation:


Then, 1200 x 1 + R 2= 1348.32

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100

1 +R

2=134832

=11236

100 120000 10000

1 +R

2=106

2100 100

1 +R

=106

100 100

R = 6%

DATA SUFFICIENCY PROBLEM

Directions to Solve

Each of the questions given below consists of a statement and / or a question and two statementsnumbered I and II given below it. You have to decide whether the data provided in thestatement(s) is / are sufficient to answer the given question. Read the both statements and

Give answer (A) if the data in Statement I alone are sufficient to answer the question,while the data in Statement II alone are not sufficient to answer the question.

Give answer (B) if the data in Statement II alone are sufficient to answer the question,while the data in Statement I alone are not sufficient to answer the question.

Give answer (C) if the data either in Statement I or in Statement II alone are sufficient toanswer the question.

Give answer (D) if the data even in both Statements I and II together are not sufficient toanswer the question.

Give answer(E) if the data in both Statements I and II together are necessary to answerthe question.

1. What is the rate of compound interest?I. The principal was invested for 4 years.

II. The earned interest was Rs. 1491.A.I alone sufficient while II alone not sufficient to answer





Answer: Option D

Explanation:

Let Principal = Rs. P and Rate = R% p.a. Then,

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Amount = Rs. P 1 +R

4100

C.I. =P 1 +R

4- 1100

P 1 +R

4- 1 = 1491.100

Clearly, it does not give the answer.


2. What will be compounded amount?I. Rs. 200 was borrowed for 192 months at 6% compounded annually.

II. Rs. 200 was borrowed for 16 years at 6%.A.I alone sufficient while II alone not sufficient to answer




E.Both I and II are necessary to answ

Answer: Option C

Explanation:

I. Amount = Rs. 200 x 1 +6

16100

II. Amount = Rs. 200 x 1 +6

16100

Thus, I as well as II gives the answer.

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EXERCISE PROBLEMS

1. The least number of complete years in which a sum of money put out at 20% compound interestwill be more than doubled is:

A.3 B.4

C.5 D.6

Answer: Option B

Explanation:

P 1 +20

n> 2P6

n> 2.100 5

Now,6x6x6x6

> 2.5 5 5 5

So, n = 4 years.

2. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interestrate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

A.Rs. 8600 B.Rs. 8620

C.Rs. 8820 D.None of these

Answer: Option C

Explanation:

Amount= Rs. 8000 x 1 +5

2100

= Rs. 8000 x21

x21

20 20= Rs. 8820.

3. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payablehalf-yearly is:

A.6.06% B.6.07%

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C.6.08% D.6.09%

Answer: Option D

Explanation:

Amount of Rs. 100 for 1 yearwhen compounded half-yearly

= Rs. 100 x 1 +3

2 = Rs. 106.09100

Effective rate = (106.09 - 100)% = 6.09%

4. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compoundinterest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

A.Rs. 1550 B.Rs. 1650

C.Rs. 1750 D.Rs. 2000

Answer: Option C

Explanation:

C.I.= Rs. 4000 x 1 +10

2- 4000100

= Rs. 4000 x11

x11

- 400010 10

= Rs. 840.

Sum = Rs.420 x 100

= Rs. 1750.3 x 8

5. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is thecompound interest on the same at the same rate and for the same time?

A.Rs. 51.25 B.Rs. 52

C.Rs. 54.25 D.Rs. 60

Answer: Option A

Explanation:

Sum = Rs.50 x 100

= Rs. 500.2 x 5

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Amount= Rs. 500 x 1 +5

2100

= Rs. 500 x21

x21

20 20= Rs. 551.25

C.I. = Rs. (551.25 - 500) = Rs. 51.25

6.The difference between simple interest and compound on Rs. 1200 for one year at 10% per annumreckoned half-yearly is:

A.Rs. 2.50 B.Rs. 3

C.Rs. 3.75 D.Rs. 4

E.None of these

Answer: Option B

Explanation:

S.I. = Rs1200 x 10 x 1

= Rs. 120.100

C.I. = Rs. 1200 x 1 +5

2- 1200 = Rs. 123.100

Difference = Rs. (123 - 120) = Rs. 3.

7. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2years is Rs. 96. What is the rate of interest per annum?

A.8 B.10

C.12 D.Cannot be determined

E.None of these

Answer: Option A

Explanation:

15000 x 1 +R

2- 15000 -15000 x R x 2

= 96100 100

=15000 1 +R

2- 1 -2R

= 96100 100

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15000(100 + R)2 - 10000 - (200 x R)

= 9610000

R2 =96 x 2

= 643

R = 8.

Rate = 8%.

8. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simpleinterest on the same sum for double the time at half the rate percent per annum is:

A.Rs. 400 B.Rs. 500

C.Rs. 600 D.Rs. 800

Answer: Option B

Explanation:

Let the sum be Rs. P.

Then, P 1 +10

2- P = 525100

P11

2- 1 = 52510

P =525 x 100

= 2500.21

Sum = Rs . 2500.

So, S.I. = Rs.2500 x 5 x 4

= Rs. 500100

9. What will Rs.1500 amount to in three years if it is invested in 20% p.a. compoundinterest, interest being compounded annually?(A) 2400 (B) 2592 (C) 2678 (D) 2540

Answer -Option (B)

Solution:

The usual way to find the compound interest is given by the formula A = .In this formula, A is the amount at the end of the period of investment

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P is the principal that is investedr is the rate of interest in % p.aAnd n is the number of years for which the principal has been invested.

In this case, it would turn out to be A == 2592.

10. If a sum of money grows to 144/121 times when invested for two years in a schemewhere interest is compounded annually, how long will the same sum of money take to trebleif invested at the same rate of interest in a scheme where interest is computed using simpleinterest method?

(A) 9 years (B) 22 years (C) 18 years (D) 33 years

Answer - Option(B)

Solution

The sum of money grows to times in 2 years.

If P is the principal invested, then it has grown to P in two years when invested in compoundinterest.

In compound interest, if a sum is invested for two years, the amount is found using the followingformula

= P in this case.

=> => => =>

If r = , then in simple interest the time it will take for a sum of money to treble is found outas follows:

Let P be the principal invested. Therefore, if the principal trebles = 3P, the remaining 2P hascome on account of simple interest.

Simple Interest = , where P is the simple interest, r is the rate of interest and ‘n’ is thenumber of years the principal was invested.

Therefore, 2P = => 2 = or n = 22 years.

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11.The population of a town was 3600 three years back. It is 4800 right now. What will bethe population three years down the line, if the rate of growth of population has beenconstant over the years and has been compounding annually?

(A) 6000 (B) 6400 (C) 7200 (D) 9600

Answer - Option(B)

Solution:

The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 duringthree year span.

Therefore, the rate of growth for three years has beenThe rate of growth during the next three years will also be the same.

Therefore, the population will grow from 4800 by = 1600Hence, the population three years from now will be 4800 + 1600 = 6400

12. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly.Income tax at the rate of 20% on the interest earned is deducted at the end of each year.Find the amount at the end of the third year.

(A) 5624.32 (B) 5630.50 (C) 5788.125 (D) 5627.20

Answer – Option (A)

Solution:

5% is the rate of interest. 20% of the interest amount is paid as tax. That is 80% of the interestamount stays back. Therefore, if we compute the rate of interest as 80% of 5% = 4% p.a., we willget the same value.

The interest accrued for 3 years in compound interest = 3*simple interest on principal +3*interest on simple interest + 1*interest on interest on interest. = 3*(200) + 3*(8) + 1*0.32 =600 + 24 + 0.32 = 624.32

The amount at the end of 3 years = 5000 + 624.32 = 5624.32

13. The difference between the compound interest and the simple interest on a certain sumat 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3years?

Answer –Option (D)

(A) 9000 (B) 6250 (C) 8530.80 (D) 8780.80

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Solution:

, when interest is reckoned using compound interest, interest being compounded annually. Thedifference in the simple interest and compound interest for two years is on account of the interestpaid on the first year's interest

Hence 12% of simple interest = 90 => simple interest = =750.

As the simple interest for a year = 750 @ 12% p.a., the principal = = Rs.6250.

If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simpleinterest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 +3(750) + 3(90) + 1(10.80) = 8780.80.

14. Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9years is equal to Ram's share at the end of 11 years, compounded annually at the rate of5%. Find the share of Shyam.

(A) 2088 (B) 2000

(C) 3087 (D) None of these

Answer –Option (C)Solution:Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11

Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400

Therefore Shyam's share = (441/841) * 5887 = 3087.

15. The question for the day is from the topic simple and compound interest. Shawninvested one half of his savings in a bond that paid simple interest for 2 years and receivedRs.550 as interest. He invested the remaining in a bond that paid compound interest,interest being compounded annually, for the same 2 years at the same rate of interest andreceived Rs.605 as interest. What was the value of his total savings before investing in thesetwo bonds?

(A) Rs.5500 (B) Rs.11000

(C) Rs.22000 (D) Rs.2750

Answer - Option (D)

Solution:Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying

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bond as the interest that he received in the first year also earned interest in the second year.

The extra interest earned on the compound interest bond = Rs.55

The interest for the first year = = Rs.275

Therefore, the rate of interest = = 20% p.a.

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.

If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the

bonds = = 1375.

As he invested equal sums in both the bonds, his total savings before investing = 2*1375 =Rs.2750.

16. Rs.100 doubled in 5 years when compounded annually. How many more years will ittake to get another Rs.200 compound interest?

(A)10 years (B) 5 years (C) 7.5 years (D) 15 years (E) 8 years

Answer - Option (B)

Solution

Rs.100 invested in compound interest becomes Rs.200 in 5 years.

The amount will double again in another 5 years.

i.e., the amount will become Rs.400 in another 5 years.

So, to earn another Rs.200 interest, it will take another 5 years.

Correct answer choice (2).

17. Find the effective rate of interest for an investment that earns 512% per year, compounded continuously.

Solution:

We are not given a value of P in this problem, so either pick a valuefor P and stick with that throughout the problem, or just let P = P.We have that t = 1, and r = .055. To find the effective rate of interest,

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first find out how much money we have after one year:A = PertA = Pe(.055)(1)A = 1.056541P.Therefore, after 1 year, whatever the principal was, we now have 1.056541P.Next, find out how much interest was earned, I, by subtracting the ini-tial amount of money from the final amount:I = A − P= 1.056541P − P= .056541P.Finally, to find the effective rate of interest, use the simple interestformula, I = Prt. So,I = Pr(1) = .056541P.056541 = r.

Therefore, the effective rate of interest is 5.65%.

DATA SUFFICIENCY PROBLEM

1. An amount of money was lent for 3 years. What will be the difference between the simpleand the compound interest earned on it at the same rate?

I. The rate of interest was 8 p.c.p.a.II. The total amount of simple interest was Rs. 1200.

A.I alone sufficient while II alone not sufficient to answer




E. Both I and II are necessary to answer

Answer: Option E

Explanation:

Given: T = 3 years.

I. gives: R = 8% p.a.

II. gives: S.I. = Rs. 1200.

Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.

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Difference between C.I. and S.I. may be obtained.

So, the correct answer is (E).

2.What will be the compound interest earned on an amount of Rs. 5000 in 2 years?I. The simple interest on the same amount at the same rate of interest in 5 years is Rs.

2000.II. The compound interest and the simple interest earned in one year is the same.

III. The amount becomed more than double on compound interest in 10 years.A.I only

B.I and II only

C.II and III only

D.I and III only

E. None of these

Answer: Option A

Explanation:

P = Rs. 5000 & T = 2 years.

I. S.I. on Rs. 5000 in 5 years is Rs. 2000.

5000 x R x 5= 2000 R = 8.

100

Thus I only gives the answer.

Correct answer is (A).

3.What is the rate of interest p.c.p.a.?I. An amount doubles itself in 5 years on simple interest.

II. Difference between the compound interest and the simple interest earned on a certainamount in 2 years is Rs. 400.

III. Simple interest earned per annum is Rs. 2000.A.I only

B.II and III only

C.All I, II and III

D.Any two of the three

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E. I only or II and III only

Answer: Option E

Explanation:

I.P x R x 5

= P R = 20.100

II. P 1 +R

2- P -P x R x 2

= 400 PR2 = 4000000.100 100

III.P x R x 1

= 2000 PR = 200000.100

PR2

=4000000

R = 20.PR 200000

Thus I only or (II and III) give answer.


4. Mr. Gupta borrowed a sum of money on compound interest. What will be the amount tobe repaid if he is repaying the entire amount at the end of 2 years?

I. The rate of interest is 5 p.c.p.a.II. Simple interest fetched on the same amount in one year is Rs. 600.

III. The amount borrowed is 10 times the simple interest in 2 years.A.I only

B.III only

C.I or II only

D.II and Either I or III only

E.

All I, II and III are required

Answer: Option D

Explanation:

I. gives, Rate = 5% p.a.

II. gives, S.I. for 1 year = Rs. 600.

III. gives, sum = 10 x (S.I. for 2 years).

Now I, and II give the sum.

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For this sum, C.I. and hence amount can be obtained.

Thus, III is redundant.

Again, II gives S.I. for 2 years = Rs. (600 x 2) = Rs. 1200.

Now, from III, Sum = Rs. (10 x 1200) = Rs . 12000.

Thus, Rate =100 x 1200

= 5% p.a.2 x 12000

Thus, C.I. for 2 years and therefore, amount can be obtained.

Thus, I is redundant.

Hence, I or III redundant.

5.What is the compound interest earned at the end of 3 years?I. Simple interest earned on that amount at the same rate and for the same period is

Rs. 4500.II. The rate of interest is 10 p.c.p.a.

III. Compound interest for 3 years is more than the simple interest for that period by Rs.465.

A.I and II only

B.II and III only

C.I and III only

D.Either II or III only

E.Any two of the three

Answer: Option D

Explanation:

I. gives, S.I for 3 years = Rs. 4500.

II. gives, Rate = 10% p.a.

III. gives, (C.I.) - (S.I.) = Rs. 465.

Clearly, using I and III we get C.I. = Rs. (465 + 4500).

Thus, II is redundant.

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Also, from I and II, we get sum =100 x 4500

= 15000.10 x 3

Now C.I. on Rs. 15000 at 10% p.a. for 3 years may be obtained.

Thus, III is redundant.

Either II or III is redundant.

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