JAMB Mathematics 2023 Paper

Concept:Simple interest is calculated on the original principal only, so the extra amount over the deposit is the interest earned.Explanation:Let the principal be $P$ and the annual interest rate be $R\%$.Simple interest formula is $I = \frac{PRT}{100}$.For $T = 10$ years, the amount becomes $3P$, so the interest earned is $I = 3P - P = 2P$.Thus, $2P = \frac{P \times R \times 10}{100}$.Dividing both sides by $P$: $2 = \frac{R \times 10}{100} = \frac{R}{10}$.So $R = 20\%$.Now, for the amount to become $5P$, the interest needed is $I = 5P - P = 4P$.Using the same rate, $4P = \frac{P \times 20 \times T}{100} = \frac{PT}{5}$.Cancel $P$: $4 = \frac{T}{5}$.Therefore, $T = 20$ years.Answer:C. 20 years