Compound Interest – Definition, Formula, Solved Examples

Compound Interest, in general, is the Interest Calculated on a Principal and the Interest Accumulated over the Previous Period. It is not similar to the Simple Interest where Interest is not added. Get to know the Compound Interest Formula, Procedure on How to find the Compound Interest on a Daily, Monthly, Quarterly, Yearly Basis. Check out the Solved Examples explained step by step for a better understanding of the concept.

Compound Interest Definition

In Simple Words, Compound Interest is nothing but the Interest that adds back to the Principal Sum so that Interest will be earned during the next compounding period.

Formula to Calculate Compound Interest

Compound Interest Formula is given by Compound Interest = Amount – Principal

Amount A = P(1+r/n)^nt

where,

A= Amount

P= Principal

R= Rate of Interest

n = number of times the interest is compounded per year.

Compound Interest When Interest is Compounded Annually

The Amount Formula mentioned above is the general formula for the number of times the principal is compounded in a year. If the Amount is Compounded Yearly or Annually then Amount Formula is given by

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

Compound Interest (CI) when Interest is Compounded Half-Yearly

In this case, if  R is the Rate of Interest Per Annum then it is clearly R/2 per half-year.
A = P(1 + (R/2)/100)^2*1

R/2 = R^‘

CI = A – P

= P(1 + (R/2)/100)^2*1 – P

In the Cases, When the Rate is compounded Half-Yearly, we divide the rate by 2 and multiply the time by 2 before using the general formula for the amount in case of the compound interest.

Compound Interest when Interest is Compounded Quarterly

Let us consider the Compound Interest on a Principal P kept for 1 Year and Interest Rate is R %. Since the Interest is Compounded Quarterly Principal Amount will be changed after 3 months. Interest for the Next Three Months will be calculated on the Amount after 3 first months.

In the same way, Interest for Third Quarter will be calculated on the amount left after the first 6 months. Last Quarter will be calculated on the amount remaining after the first 9 months.

A = P(1+ (R/4)/100)^4T

CI = A – P

= P(1+ (R/4)/100)^4T – P

Solved Example Questions on Compound Interest

1. A town had 15,000 residents in 2000. Its population declines at a rate of 10% per annum. What will be its total population in 2004?

Solution:

The population of a town decreases by 10% every year. Thus, the population of a town next year is calculated on the current year. For Decrease, we have the formula

A = P(1-R/100)ⁿ

= 15000(1-10/100)⁴

= 15000(0.9)⁴
= 9841

The population of the town in 2004 is 9841.

2. The price of a radio is Rs 2000 and it depreciates by 5% per month. Find its value after 4 months?

Solution:

For depreciation, the Amount is A = P(1-R/100)ⁿ

= 2000(1-5/100)⁴

= 2000(1-0.05)⁴

=2000(0.95)⁴
= 1629

Price of radio is Rs. 1629 after 4 months.

3. Calculate the compound interest (CI) on Rs. 10000 for 2 years at 5% per annum compounded annually?

Solution:

We know the formula for Compound Interest Annually is

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

= 10000(1+5/100)²

= 10000(105/100)²

= 10000(1.1025)

= 11025

CI = A – P

= 11025 – 10000

= Rs. 1025

4. Calculate the compound interest to be paid on a loan of Rs. 5000 for 3/2 years at 10% per annum compounded half-yearly?

Solution:

Rate of Interest when compounded half-yearly we need to divide R by 2 and multiply Time with 2.

A = P(1+R/100)ⁿ

= P(1+R/2*100)^2*n

= 5000(1+10/2*100)^2*3/2

= 5000(1+5/100)³

= 5000(105/100)³

= 5000(1.157)

= 5788

CI = A – P

= 5788 – 5000

= 788

The Compounded Interest to be paid on a loan is Rs.788