The compound interest on a certain sum for first two successive years are Rs. 100 and Rs. 172 respectively. Find the rate of interest.

Let the sum of money = Rs. x

Rate of interest = r % p.a

N = 1 year each

Compound interest for first year = C1 = x [1 + r/100]1 – x

= x [r/100] ---(1)

∴ Amount obtained from first year = x [1 + r/100]1

Compound interest for second year C2 = x [1 + r/100]1 [1 + r/100]1 - x[1 + r/100]1

= x[1 + r/100]1 [r/100] ---(2)

From 1 and 2,

C1 = Rs. 100

⇒ x [r/100] = Rs. 100 ---(3)

C2 = Rs. 172

x (r/100) × [1 + r/100] = Rs. 172

From 3,

100 × [1 + r/100] = 172

⇒ 1 + (r/100) = 1.72

⇒ r = 72%

Thus, the rate is 72% p.a.