Simple interest on a certain sum of money for 3 years at 5% per annum is ₹ 600. Find the amount due and compound interest on this sum at the same rate after 3 years, the interest being reckoned annually.

Let P be the sum of money.

R = 5 %, T = 3 years, I = ₹ 600

$\text{S.I. for three years} = \dfrac{P \times R \times T}{100}\\[1em] ⇒ 600 = \dfrac{P \times 5 \times 3}{100}\\[1em] ⇒ 600 = \dfrac{15P}{100}\\[1em] ⇒ P = \dfrac{600 \times 100}{15}\\[1em] ⇒ P = \dfrac{60,000}{15}\\[1em] ⇒ P = 4,000$

For compound interest,

P = ₹ 4,000, R = 5 %, n = 3 years

A = P $\Big(1 + \dfrac{R}{100}\Big)^n$

= 4,000 x $\Big(1 + \dfrac{5}{100}\Big)^3$

= 4,000 x $\Big(1 + 0.05\Big)^3$

= 4,000 x $\Big(1.05\Big)^3$

= 4,000 x 1.157625

= 4,630.5

Compound Interest = Amount - Principal

= 4,630.5 - 4,000

= 630.5

Hence, the amount = ₹ 4,630.5 and compound interest = ₹ 630.5.