Compound Interest class 8 chapter6(notes) maths definition, formula

Compound Interest Definition

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period. Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well. Some of its applications are:

1. Increase or decrease in population.
2. The growth of bacteria.
3. Rise or depreciation in the value of an item.

Compound Interest Formula

The compound interest formula is given below:

Compound Interest = Amount – Principal

Where the amount is given by:

Where,

A= amount

P= principal

R= rate of interest

n= number of times interest is compounded per year

It is to be noted that the above formula is the general formula for the number of times the principal is compounded in an year. If the amount is compounded annually, the amount is given as-

                                                   A=P(1+R100)t

Let us get to know the values of Amount and Interest in case of Compound Interest for different years-

Time (in years)	Amount	Interest
1	P(1 + R/100) (R/100)	PR100
2	P(1+R100)2	P(1 + R/100) (R/100)
3	P(1+R100)3	P(1 + R/100)2 (R/100)
4	P(1+R100)4	P(1 + R/100)3 (R/100)
n	P(1+R100)n	P(1 + R/100)n-1 (R/100)

This data will be helpful in determining the interest and amount in case of compound interest easily.

NOTE

From the data it is clear that the interest rate for the first year in compound interest is the same as that in case of simple interest, ie. PR100.

Other than the first year, the interest compound annually is always greater than that in case of simple interest.

Derivation of Compound Interest Formula

Let Principal amount = P, Time = n years, Rate = R

Simple Interest (S.I.) for the first year:

SI1 = P × R × T100

Amount after first year = P + SI1 = P + P × R × T100 = P(1+R100) = P2

Simple Interest (S.I.) for second year:

SI2 = P2 × R × T100

Amount after second year = P2 + SI2 = P2 + P2 × R × T100 = P2(1 + R100) = P(1 + R100)(1 + R100)
= P(1 + R100)2

Simila

NOTE. 1. if the interest is compounded half yearly , then the time is 2T and the rate is R/2%.

2. if the interest is compounded quarterly, then the time is 4T and the rate is R/4%

3. if the interest is compounded monthly, then the time is 12T and the rate is R/12%.

 P(1 + R

P[(1 + R100                                                                                                    

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Compound Interest

Compound