Correct Answer - Option 4 : 2 years
Given:
Amount invested on simple interest = Rs. 10000
Formula:
Let P = principal, R = rate of interest and N = time period
Simple Interest = PNR / 100
Compound interest = P(1 + R / 100)n – P
Calculation:
Simple Interest earned in M years = 10000 × 24 × M / 100 = Rs. 2400M
Compound interest earned in N years = 12000(1 + 15 / 100)N – 12000
⇒ M / N = 2 / 1
⇒ M = 2N
⇒ 2400M + 12000(1 + 15 / 100)N – 12000 = 13470
⇒ 4800N + 12000(1 + 15 / 100)N – 12000 = 13470
Using trial and error,
N = 2 years and M = 4 years
Required difference = 4 – 2 = 2 years