Question

A certain sum of money at compound interest becomes rs 7396 in two years and rs 7950.70 in three yeas.Find the rate of interest.

Answer 1

When interest earned is compounded annually, then this means that even the interest will earn interest.

In this case the accumulated amount at time 2 years will be the principle for the accumulated amount in time 3 years.

This is because the interest will earn interest. And the period here will be one since from time 2 to 3 the interval is 1.

Calculations:

Let C =principal amount. =rs7396
Accumulated amount =rs7950.70

Formulae:C(1+i)=Accumulated amount.

7396(1+i)=7950.70

1+i=7950.70/7396

1+i=1.075

i=1.075-1
i=0.075

0.075×100%=7.5%

Rate=7.5%

Answer 2

Answer:

Given Amount = 7396 and T = 2 years, Amount = 7950.70 and T = 3 years.

Let the sum be a and the Annual rate of interest be b.

Given Rs.7396 in 2 years.

We know that A = P(1+r/100)^n

                  7396 = a(1+b/100)^2    ---- (1)

Given Rs.7950.70 in 3 years

A = P(1+r/100)^n

7950.70 = a(1+b/100)^3        ------ (2).

On solving (1) and (2), we get

7950.70/7396= (1+b/100)

1.07500 = 1 + b/100

0.075 = b/100

b = 7.5.

The rate of interest = 7.5%.