Question

Find the amount and the compound interest on Rs.18750 after 3 years, compounded annually, the rates of interest being 8% p.a 10% p.a and 12% p.a during the first year, second year and third year respectively.

Answer 1

The amount at the end of the first year

$A_1=P(1+\frac{R}{100})$

$=18.750(1+\frac{8}{100})$

$=18.750\cdot \frac{27}{25}$

$=750\times 27$

$=$Rs. $20,250$

Interest $I_1=A_1-P$

First year $=(20,250-16,750)$

$=$Rs. $1,500$

Amount for second year

$A_2=P(1+\frac{R_1}{100})(1+\frac{R_2}{100})$

$=18,750(1+\frac{8}{100})(1+\frac{10}{100})$

$=18,750\cdot \frac{27}{25}\cdot \frac{11}{10}$

$=$Rs. $22,275$.

Interest for second year

$=A_2-A_1$

$=22,275-20,250$

$=$Rs. $2,025$

Amount for third year

$A_3=P(1+\frac{R_1}{100})(1+\frac{R_2}{100})(1+\frac{R_3}{100})$

$=18,750(1+\frac{8}{100})(1+\frac{10}{100})(1+\frac{12}{100})$

$=18,750\times \frac{27}{25}\times \frac{11}{10}\times \frac{28}{25}$

$=$Rs. $24,948$.

Interest for third year $=A_3-A_2$

$=24,948-22,275$

$=$Rs. $2,673$.