A sum of money is lent at 8% per annum compound interest. If the interest for the second year exceeds that for the first year by ₹ 32, find the sum of money.

Let the sum (principal) = ₹ 100

For the first year :

P = ₹ 100, R = 8 %, T = 1 year

$\text{Interest for first year} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{100 \times 8 \times 1}{100}\\[1em] = \dfrac{800}{100}\\[1em] = 8$

Amount at the end of first year = P + I

= ₹ 100 + 8

= ₹ 108

For the second year :

P = ₹ 108, R = 8 %, T = 1 year

$\text{Interest for second year} = \dfrac{P \times R \times T}{100}\\[1em] = \dfrac{108 \times 8 \times 1}{100}\\[1em] = \dfrac{864}{100}\\[1em] = 8.64$

Difference between the C.I. for the first year and the C.I. for the second year = ₹ 8.64 - 8 = ₹ 0.64

Now, when the difference of interest = ₹ 0.64 , sum = ₹ 100

And, when the difference of interest = ₹ 32 , sum = ₹ $\dfrac{100}{0.64} \times 32$

= ₹ 5,000

Hence, the sum of money = ₹ 5,000.