JAMB 2023 Mathematics · Question 37

At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10…

Question

At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?

A.15 years
B.25 years
C.20 years
D.30 years

Answer: C. 20 years

Explanation written with AI and checked against the answer key

Analyze the question: With simple interest, the amount A = P + I, where I = PRT/100. After 10 years the amount is 3P, so the interest earned is 2P. We need the time at which the amount is 5P, meaning the interest is 4P. Concept: Simple interest grows by the same amount every year, so interest is directly proportional to time. Solution: Step 1: Find the interest after 10 years. A = 3P, so I = 3P − P = 2P Step 2: Find the yearly interest. 2P ÷ 10 = 0.2P per year (a rate of 20% per annum) Step 3: Find the interest needed for the amount to be 5P. I = 5P − P = 4P Step 4: Find the time. T = 4P ÷ 0.2P = 20 years Check: In 20 years the interest is 20 × 0.2P = 4P, so the amount is P + 4P = 5P ✓. The correct option is C. **Tip: In simple interest, the interest is proportional to time. If the amount is 3P, the interest is 2P (not 3P). If the amount is 5P, the interest is 4P. Since 4P is double 2P, the time is double 10 years, giving 20 years. Many students wrongly think "3 times in 10 years means 5 times in about 16.7 years", which is the mistake the options are designed to catch.

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