Question

Future Value and Compounding

1. What do we mean by the future value of an investment?
2. What does it mean to compound interest? How does compound interest differ from simple interest?

Answer 1

a)

Future value may be defined as the value of the the present amount if it was made at time in future. For example if $ 100 is deposited in bank today, and suppose the interest rate is 10 %, the future value of $100 will be $110. As the interest will be earned in the current year, the Future value will be more than the present value. It is based on the concept of compouding and time value of money.

The concept of Time value of money refers to the fact that the value of money received today is different in its value from the money to be received after one year.  If it is received today it can be reinvested and the value will become more after one year. The value of investment after one year is known as Future value.

Future value be calculated with help of below formula -

FV = PV ( 1 + r )ⁿ

where,

FV = future value

PV = present value

r = rate of interest

n = no. of years

b)

Compound interest is interest which is earned on the previous received interest. In compound interest, interest is compounded. Interest is received on interest also together with the principal amount.

More, the number of compounding more the interest will be earned.

For example - If you deposit 1000 $ today at 10 % interest rate and no further deposits are made.

Total deposits after one year will be = 100 + 10 % of 100 (interest earned)

= 100 + 10 = 110 $

( In 1st year, interest earned = 10 $)

Total deposits after two year will be = 110 + 10 % of 110 (interest is earned on total accumulated amount from last year)

= 110 + 11

= 121 $

( in 2nd year interest earned 11 $)

Compound interest is calculated as = P ( 1 + r) ⁿ - P

where,

P = Principal amount

r = rate of interest

n = No of years.

In simple interest, interest is only earned on the principal amount, not the interest earned from previous years and same interest is earned every year. The interest earned in 2nd year will be same as of 1st year and thereafter.

For example-

If you deposit 1000 $ today at 10 % interest rate and no further deposits are made.

Total deposits after one year will be = 100 + 10 % of 100 (interest earned)

= 100 + 10 = 110 $

( In 1st year, interest earned = 10 $)

Total deposits after two year will be = 110 + 10 % of 100 (interest earned)

=110 + 10 = 120 $

( In 2nd year, interest earned = 10 $)

In simple, interest same interest amount is earned in all years on the initial amount (Principal) untill any new deposits or withdrawal are made.

Simple interest is calculated as -

SI = P * R * T

where,

P = Principal amount

R = rate of interest

T = No of years.

Hope it helps !