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 I year, if the interest is reckoned half-yearly.

Answer 1

The formula for $SI=\frac{P\times n\times r}{100}$

Given SI = Rs. 450,

n = 2 and

r = 4%, we have

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

Or $P=\frac{450\times 100}{(2\times 4)}=5625$
CI for the same interest rate for 1 year, compounded every half yearly can be given by the formula

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.