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Ihtisham Jadoon Business Finance

Time Value of Money

The first concept, time value of money, says that a rupee in your hand today is worth

more than the rupee that you are going to get tomorrow or the day after. This is because if

you have a rupee in hand, you can put it into a bank (invest it and can earn interest

(return on it, and tomorrow you are going to have more than rupee one, which of course,

is more desirable than having !ust one rupee.

Time "alue of #oney$ %ny change in the value of money due to time.

%n amount worth &s.', today is always prefer on ', after one year

because of various reasons, why)

Interest

1. Simple Interest (or Straight Line):

*imple interest incurs only on the principal. +hile calculating simple interest we keep the

interest and principal separately, i.e., the interest incurred in one year is not added to the

principal while calculating interest of the net period.

Example: 1

*uppose a person deposits &s.' in a bank -/. Future value at the end of each year

using simple interest approach will be as under$

0ear Beginning amount Interest earned during period Ending amount (V)

'. ' 1!"1. ' 11#2. ''3 1$%4. '14 1&$5. '21 1%!3. '4 1%"6. '4 1'#. '53 1#%

7. '34 1$1!. 1$ " 1"!

*imple interest can be calculated using the following formula.

V *V + (*V x i x n)

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Ihtisham Jadoon Business Finance

Example: %ssume that you have &s ' today and you want to invest the amount with a

bank for five years. The bank is offering an interest rate of 6 percent. +e can obtain the

simple interest on the investment using the aforementioned formula

F " 8 9" : (9" i n

;ere F" is the simple interest accrued for the term of the investment

9" is the amount invested, i.e., &s ' in our eample

i stands for the interest rate offered by the bank, i.e., 6 / 8 .6

n is the term of the investment, which is assumed to be 5 years

9utting these values in the formula, we get

F" 8 ' : (' .6 5

F" 8 ' : (6 5

F" 8 ' : (25

F" 8 &s '25

;ere &s '25 is the future value of investment after five years and &s 25 is the interest

accrued during five years on the initial investment of &s '.

$) ,ompound Interest:

annually, ?uarterly, or monthly.

For computing the annual compounding, we use the following formula

-nnual (yearly) ompounding:

V *V x (1 + i) n

Example:1

%ssume that the investor in our previous eample is offered a compound return (interest

on his same investment, at the same interest rate and term. The future value of the

investment is given as under$

F " 8 9" (' : i n

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F" 8 ' (':.65

F" 8 ' ('.65

F" 8 ' ('.4155

F" 8 '4.155

Example:1

@ompound interest with A' initial deposit and / annual interest rate.

0ear Beginning amount Interest earned during period Ending amount (V)

'. ' 1!"1. ' .34 11#.#%2. ''3.34 7.22 1$'./

4. '15.76 '. 1.!'5. '23.5 '. 1%#./&3. '43.72 ''.65 1'".#/6. '5.37 '1.6 11.&/. '6'.27 '2.6'' 1"'.1!7. '5.' '4.' 1//./11!. 1//./1 1'.// $1'./!

n

F" 8P0 (1+ i)

%t the end of 'styear$ '(1+ i) = 108

2

%t the end of 1nd year$ '(1+ i) = 116.64

3

%t the end of 2rd year$ '(1+ i) = 125.97

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