2023 · Q53
A sum of money at 20% rate of compound interest per annum becomes more than 100 times in n years. What is the least value of n? (Use log10 2 = 0.301, log10 3 = 0.477).
Elementary MathematicsSimple and Compound Interest
- A23
- B24
- C25
- D26
Explanation
We need 1.2ⁿ > 100, i.e. n·log₁₀(1.2) > 2. Now log₁₀(1.2) = log₁₀(12/10) = log₁₀3 + 2log₁₀2 − 1 = 0.477 + 0.602 − 1 = 0.079, so n > 2/0.079 ≈ 25.3, meaning n ≥ 26. Indeed 1.2²⁵ ≈ 95.4 < 100 while 1.2²⁶ ≈ 114.5 > 100, so the least such n is 26. The answer is (D).