At what rate of simple interest per annum will a sum of money double itself in 20 years?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5%
A sum doubles when the interest equals the sum itself, that is, when the interest is 100% of the sum.
Interest in 20 years \(=r\times20\%\) of the sum
\(r\times20=100\)
\(r=100\div20=5\)
The rate is 5% per annum.
Why the other options are incorrect
Option (1) 4% — Incorrect. At 4% the interest in 20 years is \(4\times20=80\%\) of the sum, so the sum would not exactly double.
Option (2) 10% — Incorrect. At 10% the interest in 20 years is \(10\times20=200\%\) of the sum, so the sum would not exactly double.
Option (3) 6.25% — Incorrect. At 6.25% the interest in 20 years is \(6.25\times20=125\%\) of the sum, so the sum would not exactly double.