Copyright ©2015 Pearson Education, Inc. All rights reserved.


Chapter 4

Mathematics of Finance


Section 4.1

Simple Interest and Discount

4Copyright ©2015 Pearson Education, Inc. All rights reserved.

A fee that is charged by a

lender to a borrower for the

right to use the borrowed

funds. The funds can be used

to purchase a house, a car, or

goods that were charged on a

credit card, for example. The

interest charge typically is

expressed as an annual

percentage rate.

5

To furnish her new apartment, Maggie Chan borrowed $4000

at 3% interest from her parents for 9 months. How much

interest will she pay?

Solution:


Example1:

Thus, Maggie pays a total of $90 in interest.40003

0.03 90.4

I Prt

I

Use the formula with ,I Prt 4000, 0.03 a d , nP r

9 /12 3 / 4 years :t

Example2: Example3:


Example 1: A= 4000 + 90 = 4090

Example 2: A= 4500 +2565= 7065

Example 3: A= 500 + 90= 590

A2.33

A


A

8

Interest (I), Future Value (FV: A), Present

Value (P)



Section 4.2

Compound Interest

• Compound interest is interest calculated on the initial principal and also on

the accumulated interest of previous periods of a deposit or loan.

• Compound interest can be thought of as “interest on interest,” and will make a

deposit or loan grow at a faster rate than simple interest, which is interest

calculated only on the principal amount.


Suppose that $5000 is invested at an annual interest rate of

3.1% compounded continuously for 4 years. Find the

compound amount.

Solution:

Example:

.031(4)5000 $5660.08.rtP eA e

In the formula for continuous compounding let

and Then a calculator with an key shows that

5000, .031,P r

4.t xe


A=9000 𝑒0.04∗5

1.22

A=9000*1.22= 10992.64


I= PRT= 10000*.05*3= $1500

A=P+I= 10000+1500=11500

Difference between simple and compound interest

15765.25-11500= $4265.25


quarterly 44

4

0.0509 5.09


Semi annually 22

2

5.060.0506


How much do you need to invest now, to get $10,000 in 10 yearsat 8% interest rate?

PV = $10,000 / (1+0.08)10 = $10,000 / 2.1589 = $4,631.93

So, $4,631.93 invested at 8% for 10 Years grows to $10,000

Your goal is to have $2,000 in 5 Years. You can get 10%, so how much should you

start with?

PV = $2,000 / (1+0.10)5 = $2,000 / 1.61051 = $1,241.84

$1,241.84 will grow to $2,000 if you invest it at 10% for 5 years.


Section 4.3

Annuities, Future Value,

and Sinking Funds

19

A business sets up a sinking fund so that it will be able to pay

off bonds it has issued when they mature. If it deposits

$12,000 at the end of each quarter in an account that earns

5.2% interest, compounded quarterly, how much will be in the

sinking fund after 10 years?

Solution:


Example:

40

(1 ) 1

(1 .052 / 4) 112,000

.052 / 4

$624,369.81.

niS R

i

The sinking fund is an annuity, with

The future value is

12,000, .052 / 4, and R i

4(10) 40.n

So there will be about $624,370 in the sinking fund.


Section 4.4

Annuities, Present Value,

and Amortization

24

Jim Riles was in an auto accident. He sued the person at fault

and was awarded a structured settlement in which an

insurance company will pay him $600 at the end of each

month for the next seven years. How much money should the

insurance company invest now at 4.7%, compounded monthly,

to guarantee that all the payments can be made?

Solution:


Example:

841 (1 ) 1 (1 .047 /12)600 $42,877.44.

.047 /12

niP R

i

The payments form an ordinary annuity. The amount needed to

fund all the payments is the present value of the annuity. Apply the

present-value formula with

(the interest rate per month).

600, 7 12 84, and .047 /12R n i

The insurance company should invest

Copyright ©2015 Pearson Education, Inc. All rights reserved. · 2015. 12. 28. · Title: Chapter 5...

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Transcript of Copyright ©2015 Pearson Education, Inc. All rights reserved. · 2015. 12. 28. · Title: Chapter 5...