Question

A man invests Rs. 6500 at 5% compound interest for 3 years. Calculate
a) The interest for the first year
b) Amount at the end of second year
c) Interest for the third year.

Answer 1

Principal $=P=Rs.6500$

rate of interest $=r=5$% $CI$ p.a.

time $=t=3$ years

a) Interest for the first year will be the same as for the case of simple interest

$\therefore$ $I=\frac{P\times r\times t}{100}=\frac{6500\times 5\times 1}{100}=Rs.325$

(b) Amount at the end of second year the amount of the end of ${}^{\prime }{n}^{\prime }$ years is given by

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

$\therefore$ Using this we can calculate the amount of the end of two years

$\therefore$ $A=6500{(1+\frac{5}{100})}^2$

$=6500{\left(\frac{21}{20}\right)}^2$

$=\frac{6500\times 21\times 21}{400}$

$=7166.25$

(c) Interest for the third year

Amount at the end of second year $=Rs.7166.25$

$\therefore$ Interest two year $=Rs.7166.25-6500$ $=Rs.666.23$

Amount of the end of third year $=P{(1+\frac{r}{100})}^3$

$=6500\times \frac{21\times 21\times 21}{20\times 20\times 20}=Rs.7524.5625$

$\therefore$ Interest for the third year $=$ Interest for $3$ years $-$ interest for $2$ years $=1024.5625-668.25=Rs.358.3125$