Question

What is compound interest and how is it calculated?

Answer 1

Answer :

Meaning of compound interest :

In simple words , Compound interest is interest on interest.

Compound interest is the amount of interest which is calculated on the principal amount as well as on accumulated interest amount on the loan.

For example,

If Mr X has deposited $ 10,000 in a bank for three years, and Bank provides 10% per annum interest compounding annually.

First year bank will give interest on principle amount.

But next year bank will calculate interest on total amount which is principle deposit plus interest accumulated on principle amount in first year.

Calculation of compound interest :

Following formula is used to calculate compound interest:

A= P ( 1 + r/n ) ^{n * t}

where ,

A = final amount including interest

P= principle amount

r = rate of interest

n = number of compounding within a year

t = number of years.

Compound interest is obtained by substracting the initial principal amount from this final amount .

For example :

If Mr X has deposited $ 10,000 in a bank for three years, and Bank gives 10% per annum interest compounding semi - annually.

In the above example if we want to know the amount of compund interest at the end of deposit period.

We will apply above formula to get the total amount that will be accumulated at the end of deposit period.

A= P ( 1 + r/n ) ^{n * t}

A = $ 10,000 ( 1 + 0.10 / 2 ) ^2*3

A = $ 10,000 ( 1 + 0.05 ) ⁶

A= $ 10,000 * ( 1.05 ) ⁶

^{​​​​​​}A = $ 10,000 * 1.34

A = $ 13,400

Now final amount after compound interest is $ 13,400.

Compound interest = 13,400 - 10,000 = $ 3,400.

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