Question

Simple interest on a sum of money for 2 years at 4% is Rs. 450. Find compound interest on the same sum and at the same rate for 2 years.

Answer 1

The formula for $S.I=\frac{P\times r\times t}{100}$

Given SI = Rs. 450, n = 2 and r = 4%, we have

$450=\frac{2\times 4\times P}{100}P=\frac{450\times 100}{2\times 4}=5625$

CI for the same interest rate for 1 year, compounded every half yearly can be given by the formula

$A=P(1+\frac{r}{100}{)}^t$

Here, P = 5625, r = $\frac{4}{2}$ = 2% and n = 2, since there are two half-yearly compounding of the amounts.

Thus $A=5625\times (1+\frac{2}{100}{)}^2=5625\times (1.02{)}^2=5625\times 1.0404=5852.25$

Therefore, the compound interest is $A-P=5852.25-5625=227.25$

Thus, the CI for Rs. 5625 at 4% compounded half-yearly is Rs. 227.25.