1. $45,000 is deposited into a savings account. After one year, 4 months and 20 days it totals $52,500. Calculate the simple interest rate for this account.360 + 120 + 20 = 500 daysI = 52 500 45 000 = $7,500

2. How long does it take a principal of $25,000 at a simple interest rate of 5% to become $30,000?

3. Determine the simple interest rate applied to a principal over 20 years if the total interest paid equals the borrowed principal.I = P

4. How long does it take a principal payment to triple at a simple interst rate of 6%?I = 3 P

5. Find the total amount of simple interest that is paid over a perod of five years on a principal of $ 30,000 at a simple interest rate of 6%.

6. Calculate the total worth of an investment after six months with a principal of $10,000 at a simple interest rate of 3.5%.

7. If youdeposit$4000 into an accountpaying6% annual interest compoundedquarterly, how much money will bein theaccount after5years?F=4000(1+ 0.06/4)^(4)(5)=4000(1.015)^20F=5387.428. If youdeposit $6500 into an accountpaying8% annual interest compoundedmonthly, how much money will bein theaccount after7years?9. Sarah deposits $4,000 at a bank at an interest rate of 4.5% per year. How much interest will she earn at the end of 3 years?Solution:Simple Interest = 4,000 4.5% 3 = 540She earns $540 at the end of 3 years.10. Wanda borrowed $3,000 from a bank at an interest rate of 12% per year for a 2-year period. How much interest does she have to pay the bank at the end of 2 years?Solution :Simple Interest = 3,000 12% 2 = 720She has to pay the bank $720 at the end of 2 years.11. Raymond bought a car for $40, 000. He took a $20,000 loan from a bank at an interest rate of 15% per year for a 3-year period. What is the total amount (interest and loan) that he would have to pay the bank at the end of 3 years?Solution :Simple Interest = 20,000 13% 3 = 7,800At the end of 3 years, he would have to pay$20,000 + $7,800 = $27,800

12. Moho wants to invest R 30 000 into an account that offers a compound interest rate of 6% p.a. How much money will be in the account at the end of 4 years?A=P(1+i)nA=30000(1+0,06)4=37874,31Moho will have R37874,31 in the account at the end of 4 years.

13. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: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. 698.14. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?Let the sum invested in Scheme A be Rs.xand that in Scheme B be Rs. (13900 -x).Then,xx 14 x 2+(13900 -x) x 11 x 2= 3508

100100

28x- 22x= 350800 - (13900 x 22)6x= 45000x= 7500.So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

15. 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?Principal= Rs.100 x 4016.25

9 x 5

= Rs.401625

45

= Rs. 8925.

16. 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?Time =100 x 81years= 4 years.450 x 4.517. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?Let rate = R% and time = R years.Then,1200 x R x R= 432

100

12R2= 432R2= 36R = 6.18. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?S.I. = Rs. (15500 - 12500) = Rs. 3000.Rate =100 x 3000%= 6%

12500 x 4

19. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:Let the sum be Rs. 100. Then,S.I. for first 6 months = Rs.100 x 10 x 1= Rs. 5

100 x 2

S.I. for last 6 months = Rs.105 x 10 x 1= Rs. 5.25

100 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%20. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:Let the rate be R% p.a.Then,5000 x R x 2+3000 x R x 4= 2200.

100100

100R + 120R = 2200R =2200= 10.

220

Rate = 10%.21. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

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

100100 x 3

(2175 + 725) R = 33.50 x 100 x 3(2175 + 725) R = 10050(2900)R = 10050R =10050= 3.46

2900

Original rate = 3.46%22. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:Principal = Rs.100 x 5400= Rs. 15000.12 x 323. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.S.I. for 5 years = Rs.2205x 5= Rs. 3675

3

Principal = Rs. (9800 - 3675) = Rs. 6125.Hence, rate =100 x 3675%= 12%

6125 x 5

24. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?Let the principal be P and rate of interest be R%.Required ratio =P x R x 6

100

=6PR=6= 2 : 3.

P x R x 9

100

9PR9

25. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6p.a for 2 years. Find his gain in the transaction per year.Gain in 2 years= Rs.5000 x25x2-5000 x 4 x 2

4100100

= Rs. (625 - 400)

= Rs. 225.

Gain in 1 year = Rs.225= Rs. 112.50

2

26. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:C.I.= Rs.4000 x1 +102- 4000

100

= Rs.4000 x11x11- 4000

1010

= Rs. 840.

Sum = Rs.420 x 100= Rs. 1750.

3 x 8

27. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?Sum = Rs.50 x 100= Rs. 500.

2 x 5

Amount= Rs.500 x1 +52

100

= Rs.500 x21x21

2020

= Rs. 551.25

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

28. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:S.I. = Rs1200 x 10 x 1= Rs. 120.

100

C.I. = Rs.1200 x1 +52- 1200= Rs. 123.

100

Difference = Rs. (123 - 120) = Rs. 3.29. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

15000 x1 +R2- 15000-15000 x R x 2= 96

100100

150001 +R2- 1 -2R= 96

100100

15000(100 + R)2- 10000 - (200 x R)= 96

10000

R2=96 x 2= 64

3

R = 8.Rate = 830. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:Let the sum be Rs. P.Then,P1 +102- P= 525

100

P112- 1= 525

10

P =525 x 100= 2500.

21

Sum = Rs . 2500.So, S.I. = Rs.2500 x 5 x 4= Rs. 500

100

31. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1stJuly of a year. At the end of the year, the amount he would have gained by way of interest is:Amount= Rs.1600 x1 +52+ 1600 x1 +5

2 x 1002 x 100

= Rs.1600 x41x41+ 1600 x41

404040

= Rs.1600 x4141+ 1

4040

= Rs.1600 x 41 x 81

40 x 40

= Rs. 3321.

C.I. = Rs. (3321 - 3200) = Rs. 12132. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:C.I. =x1 +42-x=676x-x=51x.

100625625

S.I. =xx 4 x 2=2x.

10025

51x-2x= 1

62525

x= 625.

33. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?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 x1 +103- 1

100

= Rs.12000 x331

1000

= 3972.

34. What is the difference between the compound interests on Rs. 5000 for 1years at 4% per annum compounded yearly and half-yearly?C.I. when interestcompounded yearly= Rs.5000 x1 +4x1 +x 4

100100

= Rs.5000 x26x51

2550

= Rs. 5304.

C.I. when interest iscompounded half-yearly= Rs.5000 x1 +23

100

= Rs.5000 x51x51x51

505050

= Rs. 5306.04

Difference = Rs. (5306.04 - 5304) = Rs. 2.0435. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:Amount = Rs. (30000 + 4347) = Rs. 34347.Let the time benyears.Then, 300001 +7n= 34347

100

107n=34347=11449=1072

1003000010000100

n= 2 years.36. 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.?Amount= Rs.25000 x1 +123

100

= Rs.25000 x28x28x28

252525

= Rs. 35123.20

C.I. = Rs. (35123.20 - 25000) = Rs. 10123.2037. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?Let the rate be R% p.a.Then, 1200 x1 +R2= 1348.32

100

1 +R2=134832=11236

10012000010000

1 +R2=1062

100100

1 +R=106

100100

R = 6%38. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:P1 +20n> 2P 6n> 2.

1005

Now,6x6x6x6> 2.

5555

So,n= 4 years.

39. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?Amount= Rs.8000 x1 +52

100

= Rs.8000 x21x21

2020

= Rs. 8820.

40. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:Amount of Rs. 100 for 1 yearwhen compounded half-yearly= Rs.100 x1 +32= Rs. 106.09

100

Effective rate = (106.09 - 100)% = 6.09%41 Tim invested $ 1500 for at the rate of 6% p.a. for 7 years and 3 months. Find the amount he got back.Solution:

Principal (P) = $ 2000,

Rate (R) = 6% p.a.

Time (T) = 7 years and 3 months.

[We know, when T i.e., the time is given in months then it should be divided by 12 to convert into years].

= 7 3/12 years.

= 7 years.

= (7 4 + 1)/4 years.

= 29/4 years.

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

Simple Interest (SI) = (2000 6 29)/(100 4)

= 348000/400

= 870

Therefore,Amount = Principal + Simple Interest

= 2000 + 870

Therefore, Amount Tim got back = $ 287042. Kyle borrowed $ 3400 at the rate of 8% p.a. for 225 days. Find the interest and amount she paid.Solution:

Principal = $ 3400,

Rate = 8% p.a.

Time = 225 days.

[We know, when T i.e., the time is given in days then it should be divided by 365 to convert into years].

= 225/365 years.

Simple Interest = (P R T)/100

= (3400 8 225)/(100 365)

= 6120000/36500

= $ 167.67

Amount = Principal + Simple Interest

= 3400 + 167.67

= $ 3567.67

Therefore, Amount paid by Kyle is $ 3567.67.

And the Interest paid by Kyle is $ 167.67.43.