Compound interest is the concept of adding accumulated interest back to the principal, so that interest is
earned on interest from that moment on.
The act
of declaring interest to be principal is called compounding (i.e. interest is compounded). A loan,
for example, may have its interest
compounded every month: in this
case, a loan with Rs. 100 principal and 1% interest per month would have a
balance of Rs. 101 at the end of the
first month.
The effect of compounding depends on the frequency with which interest is compounded and the periodic
interest rate which is applied. Therefore, in
order
to define accurately the amount to be paid under a legal contract with interest, the frequency of
compounding (yearly, half-yearly, quarterly,
monthly, daily, etc.) and
the interest rate must be specified. Since most people prefer to think of rates as
a yearly percentage, most financial
institutions disclose a (notionally) comparable
yearly interest rate on deposits or advances.
Compound interest may be contrasted with simple interest, where interest is not added to the principal
(there is no compounding).
Some useful terminology
Nominal annual interest rate: This is the annual rate, unadjusted for compounding. For example, 12% annual
nominal interest compounded monthly has a
periodic
(monthly) rate of 1%. Financial institutions will usually quote this rate along with the
compounding period, when they offer you a loan or
a fixed deposit.
Effective
annual rate: This is obtai ned by restating the nominal rate to reflect the effective rate as if
annual compounding were applied. This is
the real rate of interest you
are paying (in the case of a loan), or earning (in the case of a fixed
deposit).
Formula for calculating compound interest
Where,
P = principal amount (initial investment)
r = annual nominal interest rate (as a decimal)
n = number
of times the interest is compounded per
year
t = number of years A = amount after time t.
An example: An amount of Rs. 10,000 is deposited in
a bank paying an annual interest rate of
6.5%, compounded monthly.
Find the balance after 8 years. Answer. Using the formula above, with P = 10,000, r = 6.5/100 = 0.065, n =
12, and t = 8: So, the balance after 8
years is
approximately Rs. 16,797.