2026 · Q28
A sum of money at the rate of 5% per annum compounded annually becomes n times in 100 years. What is the value of n? (Given log₁₀2 = 0.301, log₁₀3 = 0.477 and log₁₀7 = 0.845)
Elementary MathematicsSimple and Compound Interest
- A98
- B99
- C100
- DMore than 100
Explanation
The amount is n = (1.05)¹⁰⁰. Taking common logarithms, log₁₀n = 100·log₁₀(1.05) = 100(log₁₀3 + log₁₀5 + log₁₀7 − 2) = 100(0.477 + 0.699 + 0.845 − 2) = 2.1, where log₁₀5 = 1 − log₁₀2 = 0.699. So n ≈ 10^2.1 ≈ 126, which is more than 100, option D.