Question

Gautham deposited ₹45,000 in a bank. In 2 years, he recieved an interest of ₹9,450. If the interest was compounded annually, what is the rate of interest?

• A. 8% p.a.
• B. 10% p.a.
• C. 12% p.a.
• D. 14% p.a.

Answer 1

The correct option is B 10% p.a.

Given,
Principal (P) = ₹45,000
Time period (T) = 2 years
Rate of interest (R) = ?
Compound Interest (CI) = ₹9,450
Amount (A) = CI + P
= ₹45,000 + ₹9,450
= ₹54,450

The amount is calculated by,

A = $P(1+\frac{R}{100}{)}^T$
$54,450$ = $45,000(1+\frac{R}{100}{)}^2$
⇒ $\frac{54,450}{45,000}$ = $(1+\frac{R}{100}{)}^2$
⇒ $\frac{121}{100}$ = $(1+\frac{R}{100}{)}^2$
⇒ $(\frac{11}{10}{)}^2$ = $(1+\frac{R}{100}{)}^2$
⇒ $\frac{11}{10}$ = $1+\frac{R}{100}$
⇒ $\frac{R}{100}$ = $\frac{11}{10}-1$
⇒ $\frac{R}{100}$ = $\frac{1}{10}$
⇒ $R$ = 10%

Hence, the rate of interest is 10% p.a.