# Relation Between Simple Interest and Compound Interest

We have individually looked at the concepts of Simple Interest and Compound Interest. Let us now study the contrast between them.

Given principal = Rs. 10,000; Interest Rate = 20% and Time = 3 years.

S.I. for this principal will be:

20/100 x 10,000 = Rs. 2,000

Since simple interest charges on the principal amount for every time period, the combined interest for three years will be Rs. 6,000. Adding this interest to the principal we get the final amount as Rs. 16,000.

On the other hand in compound interest charges on the final amount obtained after adding interest to the principal for each time period. So after the first year on a principal of Rs. 10,000 the compound interest is Rs. 2,000. Adding it to the principal, the amount after one year is Rs. 12,000. The interest for the second year will be thus calculated on Rs. 12,000.

I = 12,000 x 1 x 20/100 = 2400

Adding this interest to the last principal we get the amount for second year as Rs. 14,400. The interest for the third year will be compounded on this amount.

I = 14,400 x 1 x 20/100 = Rs. 2,880

Adding Rs. 2,880 to the last principal we get the final amount which is Rs. 17,280.

Alternately this result can also be directly obtained by using the formula

A = P (1 + R/100) ^ n/t

Where A stands for the final amount

P is the principal amount

R is the rate of interest

t is time in years (if compounded annually)

While n stands for time periods ( in case of compounding half yearly or quarterly)

This formula originally comes down from the concept of percentage. When we talk of rate being charged at 20% it actually means an increment of Rs. 20 on every Rs. 100. Hence the amount becomes 120/100 x P. for calculating amount for a certain number of years say 3 years this amount will be multiplied with itself thrice as follows:

P [(120/100) + (120/100) + (120/100)]

Alternately, 120/100 can also be expressed as 100 + 20/100 raised to the power 3 since its added thrice :

P (100 + 20/100) ^ 3

This now takes the form of the formula mentioned earlier and can be written as P (1+R/100) ^ n/t.

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