# Compound Interest

Financial Mathematics → Interest → Simple Interest → Compound Interest

In practice, interest is allowed to earn interest itself. When interest earns interest itself, it is called “compound interest”. So, we always use compound interest formula in financial calculations.

The simple interest formula is

$A=C(1+ni)$

The total amount after 1 year (n=1) is

$A=C(1+ni)$

Now, in compound interest, the interest is allowed to earn interest itself. So, the total amount after 2 years is

Similarly, the total amount after 3 years is

And, the total amount after n years is

So, we have the compound interest formula for n years

Where,
C = Cash amount (original amount)
i = Annual interest rate
n = Time in years
A = Amount after n years (final amount)

Example 1. Suppose \$1,000 is deposited in a bank that earns compounded interest of 12% per annum. How much will be in the account after:
(a) 1 year
(b) 2 years and 4 months
Solution:
As we know that the compound interest formula is

(a) After 1 year (Put n = 1, i = 0.12)
$A=C(1+i)^n \\ =1000(1+0.12) \\ =1000(1.12) \\ =\1120$ Answer

(b) After 2 years and 4 months (Put $n=2+\frac{4}{12}=2.33,i=0.12$)
$A=C(1+i)^n \\ =1000(1+0.12)^{2.33} \\ =1000(1.302) \\ =\1302.2$ Answer

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