A man invests ₹5000 for three years at a certain rate of interest, compounded annually. At the end of one year it amounts to ₹5600. Calculate :

(i) the rate of interest per annum.

(ii) the interest accrued in the second year.

(iii) the amount at the end of the third year.

(i) Let the rate of interest be R.

Given, amount at the end of first year = ₹5600.

Interest = Amount - Principal = ₹5600 - ₹5000 = ₹600.

Interest = $\dfrac{P \times R \times T}{100}$

$\Rightarrow 600 = \dfrac{5000 \times R \times 1}{100} \\[1em] \Rightarrow 600 = 50R \\[1em] \Rightarrow R = \dfrac{600}{50} \\[1em] \Rightarrow R = 12\%.$

Hence, the rate of interest is 12% per annum.

(ii) Amount after first year = ₹5600.

Principal for second year = ₹5600.

Interest for second year = $\dfrac{5600 \times 12 \times 1}{100} = \dfrac{67200}{100}$ = ₹672.

Hence, the interest accrued in second year = ₹672.

(iii) Amount after second year = ₹5600 + ₹672 = ₹6272

Principal for third year = ₹6272.

Interest for third year = $\dfrac{6272 \times 12 \times 1}{100} = \dfrac{75264}{100}$ = ₹752.64

Amount after third year = ₹6272 + ₹752.64 = ₹7024.64

Hence, the amount at the end of third year = ₹7024.64