Compound Interest

Aptitude

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Compound interest in short is interest on interest.

Important terms

Principal

This is the sum of money invested or the amount we borrow from the bank or someone.

Rate

This represents the rate of interest (generally in per annum). It is used to calculate the interest amount.

Time

This is the time for which the principal is invested or borrowed.

Interest

This is the amount that is calculated on the principal using the rate of interest and the time of investment.

Lets take an example to understand compound interest better.

Example

Lets say we have invested Rs. 1000 at 10% p.a. for 2 years as compound interest.

So, principal P = 1000, rate R = 10 and time n = 2.

Now, lets find the compound interest.

1st year
--------------------
Principal for 1st year P = 1000
Rate R = 10

Interest I = PRn/100,    where n = 1 as we are calculating interest for 1 year

or, I = (1000 x 10 x 1) / 100
      = 100

Amount at the end of 1st year
A = P + I
  = 1000 + 100
  = 1100

2nd year
--------------------
Principal for 2nd year = Amount at the end of 1st year
P = 1100

Rate = 10

Interest I = PRn/100,    where n = 1 as we are calculating interest for 1 year

or, I = (1100 x 10 x 1) / 100
      = 110

Amount at the end of 2nd year
A = P + I
  = 1100 + 110
  = 1210

So, after 2 years of investment the principal Rs. 1000 amounts to Rs. 1210.

So, compound interest earned in 2 years on Rs. 1000 at 10% p.a. is (1210 - 1000) i.e. Rs. 210.

Simple Interest for 1 years and Compound interest for 1 year for a given principal and rate of interest are both equal.

Important formula

Interest compounded annually

This means we are calculating the interest once a year.

Interest compounded half-yearly

This means we are calculating the interest twice a year.

Interest compounded quarterly

This means we are calculating the interest 4 times a year.

Interest compounded monthly

This means we are calculating the interest every month for a year.

Exercise #1

Rs. 1000 is invested for 2 years at 10% p.a. compounded annually. Find the compound interest.

We have,
Principal P = 1000
Rate R = 10
Time n = 2

Since, the interest is compounded annually
so, we are calculating interest once a year.

Amount A = P ( 1 + R/100 )ⁿ
 = 1000 ( 1 + 10/100 )²
 = 1000 ( 1.1 )²
 = 1000 x 1.21
 = 1210

So, compound interest CI = A - P
 = 1210 - 1000
 = 210

So, the compound interest after 2 years of investment is Rs. 210.

Exercise #2

Rs. 1000 is invested for 2 years at 10% p.a. compounded half-yearly. Find the compound interest.

We have,
Principal P = 1000
Rate R = 10
Time n = 2

Since, the interest is compounded half-yearly
so, we are calculating interest twice a year.

Amount A = P ( 1 + ((R/2) / 100) )²ⁿ
 = 1000 ( 1 + ((10/2) / 100) )^2x2
 = 1000 ( 1 + (5/100) )⁴
 = 1000 ( 1.05 )⁴
 = 1000 x 1.21550625
 = 1215.51

So, compound interest CI = A - P
 = 1215.51 - 1000
 = 215.51

So, the compound interest after 2 years of investment is Rs. 215.51.

Exercise #3

Rs. 1000 is invested for 2 years at 10% p.a. compounded quarterly. Find the compound interest.

Try this yourself.

Answer: Rs. 218.40

Exercise #4

Rs. 1000 is invested for 2 years at 10% p.a. compounded monthly. Find the compound interest.

Try this yourself.

Answer: Rs. 220.39

Important formula

Feel free to check out Compound Interest calculator.

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