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Chapter# 8 (page# 300)

Mathematics of Finance

Lecture 9

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(8. 1) Interest and it’s computation(c) The power of Compound Growth [page# 305]: As we already discussed that compound interest is greaterthan simple interest. Figure (8.1) illustrates the growth ina $10,000 investment which earns interest at 10% per yr.over a period of 10 yr. Notice that in figure, compoundinterest provides greater value as compare to simpleinterest. Also notice that if the frequency ofcompounding is increased it cause a greater value ininvestment.This suggests that value of investment is increase if:

(i) Interest rate is increase. [as shown in fig (8.2) pg 306]

(ii) Frequency of compounding is increase.

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(8. 2) Single payment computation [page 308](a) Compound Amount or Future Value

If an amount of money P   (Principal or Present Value)

earns interest compounded at a rate of ith % per period, it will grow after n  periods to the compound amount orFuture Value S, which we defines as:

Example 3 (page 310): Do yourself

Section 8.2 [page 317] Q#1: A sum of $8000 is invested in asavings account which pays interest at a rate of 9% per yr

compounded annually. If the amount is kept on depositfor 6 yrs, what will the compound amount equal? Howmuch interest will be earned during 6 yrs?

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Example 4 (page 311): Do yourself

Section 8.2 [page 317] Q#5: A company invests

$5,00,000 in a money market fund which is expectedto yield interest at a rate of 10% per yr compoundedquarterly. If the rate projections are valid, to whatamount should the $5,00,000 grow over the next 10

 yrs? How much interest will be earned during thisperiod?

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Section 8.2 [page 318] Q#15: If a saving account awardinterest of 6% per yr compounded quarterly, what amountmust be deposited today in order to accumulate $20,000after 5 yrs? How much interest will be earned during this

period?

Example 5 (page 313): Do yourself

Q# 3,7, 11, 13, 17,19,21 & 23 [Do yourself]

For Quiz#2 (11 May, 2014) [Section 8.1, Questions &Practice above questions]

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(8. 2) Single payment computation

(b) Effective Rate of Interest [page 316]

 When compounding is done more frequently than

annually. In this case, we define effective annual interestrate by r and may be computed as:

If P be the principal amount invested at a ith nominalinterest rate (interest rate) for n  yrs and m be the no. ofcompounding periods per, then the compound amountsfor effective annual interest rate and nominal interestrate will be equals, if:

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8.3 Annuities & Their future value [page 319](a) Definition: An annuity is a series of periodicpayments. Examples include reg ular deposits to a savingaccount, monthly car finance installation, mortgage ,

insurance payments etc. Although an annuity may vary interm of payments & periodic payments period, but weconsider here for the sake of simplicity equal payments &constant periodic payments period.

(b) Sum of an Annuity: We define sum of annuity (annuityimmediate) as:

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 Where,

R = amount of an annuity

Sn = Sum (future value) of the annuity after n

periods (payments)Section 8.3 [page 324] Q#1: A Person wishes to deposit$5000 per yr in a saving account which earns interest of8% per yr compounded annually. Assume the first deposit

is made at the end of this current yr & additional depositsat the end of each

(a) To what sum will the investment grow at the time of

10th

 deposit?(b) How much interest will be earned?

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