At what rate of simple interest per annum will a sum of money double itself in 12.5 years?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8%
A sum doubles when the interest equals the sum itself, that is, when the interest is 100% of the sum.
Interest in 12.5 years \(=r\times12.5\%\) of the sum
\(r\times12.5=100\)
\(r=100\div12.5=8\)
The rate is 8% per annum.
Why the other options are incorrect
Option (2) 6% — Incorrect. At 6% the interest in 12.5 years is \(6\times12.5=75\%\) of the sum, so the sum would not exactly double.
Option (3) 12.5% — Incorrect. At 12.5% the interest in 12.5 years is \(12.5\times12.5=156.25\%\) of the sum, so the sum would not exactly double.
Option (4) 10% — Incorrect. At 10% the interest in 12.5 years is \(10\times12.5=125\%\) of the sum, so the sum would not exactly double.