Question

At what rate per cent per annum will Rs. 6,000 amount to Rs. 6,615 in 2 years when interest is compounded annually ?

Answer 1

Given that:

A = ₹6,615

P = ₹6,000

T = 2 years

R = ?

When the interest is compounded annually

Amount= P$(1+\frac{R}{100}{)}^n$

⇒ 6,615 = 6000[$(1+\frac{R}{100}{)}^2$

⇒ $\frac{6,615}{6,000}$= $(\frac{100+R}{100}{)}^2$

⇒ $\frac{441}{400}$ = $(\frac{100+R}{100}{)}^2$

Taking squareroot on both sides;

⇒ $\sqrt{\frac{441}{400}}$ = $\frac{100+R}{100}$

⇒ $\frac{21}{20}$ = $\frac{100+R}{100}$

⇒ 21 × 100 = 20(100+R)

⇒ 2,100 = 2,000 + 20R

⇒ 2,100 - 2,000 = 20R

⇒ 100 = 20R

⇒ R = $\frac{100}{20}$

⇒ R = 5 % p.a.