A person invests ₹ 5,000 for two years at a certain rate of interest compounded annually. At the end of one year, this sum amounts to ₹ 5,600. Calculate:

(i) the rate of interest per annum.

(ii) the amount at the end of the second year.

(i) For 1st year:

P = ₹ 5,000

T = 1 year

A = ₹ 5,600

As we know,

$\text{A = P + S.I.}\\[1em] \Rightarrow 5,600 = 5,000 + S.I.\\[1em] \Rightarrow S.I. = 5,600 - 5,000\\[1em] \Rightarrow S.I. = 600$

Let the rate be $r$

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow 600 = ₹ \Big(\dfrac{5,000 \times r \times 1}{100}\Big)\\[1em] \Rightarrow 600 = ₹ \Big(\dfrac{5,000r}{100}\Big)\\[1em] \Rightarrow 600 = 50r\\[1em] \Rightarrow r = \dfrac{600}{50}\\[1em] \Rightarrow r = 12$

Hence, rate of interest = 12%.

(ii) For 2nd year:

P = ₹ 5,600

R = 12%

T = 1 year

$\text{Interest} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = ₹ \Big(\dfrac{5,600 \times 12 \times 1}{100}\Big)\\[1em] = ₹ \dfrac{67,200}{100}\\[1em] = ₹ 672$

$\text{Final amount = P + Interest}\\[1em] = ₹ (5,600 + 672) \\[1em] = ₹ 6,272$