# INTERESTS

Interests are of two types –

• Simple Interests
• Complex/Compounded Interests

SIMPLE INTERESTS

Simple interests are interests in which the interest on interests is not generated. For e.g. If you deposits 1000 on 10% interests for 4 year. The interest generated at the end of 4 year will be

= (number of year) * (interests percentage /100) * Base amount

= 4 * (10/100) * 1000

= 400

Total interests you will get at the end of 4 year will be 400.

Note that there are no interests paid on any of the interest amount i.e. 400.

In case of Simple interest the amount received at the end can be calculated using below formula –

Total amount received in case of Simple interest = P (1 + rt)

Where P = base amount

, r = rate of interest

, t = number of year

In case of Simple interest the total interests can be calculated using below formula –

Total interests received in case of Simple interest = P *r *t

Where P = base amount

, r = rate of interest

, t = number of year

COMPLEX/COMPOUNDED INTERESTS

Complex/Compounded interests are interests in which the interest on interests is generated. For e.g. If you deposits 1000 on 10% interests for 4 year compounded annually.

At the end of 1st year the interests will be

= (Interest percentage /100) * Base amount

= (10/100) * 1000

= 100

Now this 100 will be added to the base amount for 2nd year. Hence the base amount for 2nd year will become 1000 + 100 = 1100

For the 2nd year the interests will be

= (Interest percentage /100) * Base amount

= (10/100) * 1100

= 110

Now this 110 will be added to the base amount for 3rd year. Hence the base amount for 3rd year will become 1100 + 110 = 1210

For the 3rd year the interests will be

= (Interest percentage /100) * Base amount

= (10/100) * 1210

= 121

Now this 121 will again be added to the base amount for 4th year. Hence the base amount for 4th year will become 1210 + 121 = 1331

For the 3rd year the interests will be

= (Interest percentage /100) * Base amount

= (10/100) * 1331

= 133.1

Now the total amount received at the end of 4th year = 1331 + 133.1 = 1464.1

Hence the total interests received at the end of 4th year

= Total amount received – Principal amount

= 1464.1 -1000

= 464.1

Note that on each year the interests earned from the last year has been added to the base amount. This has resulted in generating interests on interests.

NOTE –In both the e.g. of simple and complex interest we have deposited same amount 1000 for the same term 4 year on same interest rate annually 10%. Still we received different amount. This is because, in complex interests we get interest on interest while in simple interests the interest is always calculated on the initial amount deposited.

In case of Complex interest the amount received at the end can be calculated using below formula –

Total amount received in case of Complex interest = P (1 + r/n)^nt

Where P = base amount

, r = rate of interest

, t = number of year

, n = number of time the interest will be compounded in a year

In case of Complex interest the total interests can be calculated using below formula –

Total interests received in case of Complex interest = n [(A/P)^(1/nt) – 1]

Where P = base amount

, t = number of year

, n = number of time the interest will be compounded in a year

, A = total amount received at the end