A man invests ₹ 3,000 for three years at compound interest. After one year, the money amounts to ₹ 3,240. Find the rate of interest and the amount (to the nearest rupee) due at the end of 3 years.

Let R be the rate of interest.

For the first year:

P = ₹ 3,000, R = R %, T = 1 years, A = ₹ 3,240

Compound Interest = Amount - Principal

= ₹ 3,240 - ₹ 3,000

= ₹ 240

$\text{Interest for first year} = \dfrac{P \times R \times T}{100}\\[1em] ⇒ 240 = \dfrac{3,000 \times R \times 1}{100}\\[1em] ⇒ 240 = 30 \times R\\[1em] ⇒ R = \dfrac{240}{30}\\[1em] ⇒ R = 8$

P = ₹ 3,000, R = 8 %, T = 3 years

Amount in 3 years = P $\Big(1 + \dfrac{R}{100}\Big)^n$

= 3,000 x $\Big(1 + \dfrac{8}{100}\Big)^3$

= 3,000 x $\Big(1 + 0.08\Big)^3$

= 3,000 x $(1.08)^3$

= 3,000 x 1.259

= 3,779

Hence, the rate of interest = 8 % and the amount = ₹ 3,779.