Question

A person invests ₹ 10,000 for two years at a certain rate of interest compounded annually. At the end of one year this sum amounts to ₹ 11,200 ,Calculate;

(i) the rate of interest per annum

(ii) the amount at the end of the second year

• A. (i) 12 % (ii) ₹ 10,000
• B. (i) 10 % (ii) ₹ 12,000
• C. (i) 12 % (ii) ₹ 12,000
• D. (i) 12 % (ii) ₹ 12,544

Answer 1

The correct option is D

(i) 12 % (ii) ₹ 12,544

Let the rate of interest be r
A= P(1 + $\frac{r}{100}{)}^n$

Given that A = ₹ 11,200 P = ₹ 10,000 n = 1 year

11,200 = 10,000(1 + $\frac{r}{100}{)}^1$
$\frac{11,200}{10,000}$ = (1 + $\frac{r}{100})$
$\frac{112}{100}$ = ( $\frac{100+r}{100})$
r = 112 - 100
= 12 %

(ii) A= P(1 + $\frac{r}{100}{)}^n$
= 10000(1 + $\frac{12}{100}{)}^2$
= 10000($\frac{100+12}{100}$)
= ₹ 12,544