If a principal amount doubles in 5 years at compound interest, how many years will it take for the amount to become eight times the original at the same interest rate?

Explanation

Assume the principal is Rs x and the interest rate is R% per annum. After 5 years, the amount doubles: x × (1 + R/100)^5 = 2x, so (1 + R/100)^5 = 2. To find the time t when the amount is 8 times the principal: x × (1 + R/100)^t = 8x, which means (1 + R/100)^t = 8 = 2^3. Since (1 + R/100)^5 = 2, it follows that (1 + R/100)^t = (1 + R/100)^{5×3} = (1 + R/100)^{15}. Therefore, t = 15 years.