How many years will it take for a sum of money to grow 4 times at the effective rate of 6% ?
[Use log 2 = 0.3010, log(1.06) = 0.0253]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 23.79
At an effective rate of 6% per year, a sum P grows to \(P(1.06)^n\) in n years. For it to become 4P:
\((1.06)^n = 4\)
Taking logarithms:
\(n\log(1.06) = \log 4 = 2\log 2\)
\( \displaystyle n = \frac{2\times 0.3010}{0.0253} = \frac{0.6020}{0.0253} \)
\( n = 23.79 \) years (to two decimal places)