Find the sum for which $1,250.00 will amount to$ 2,031.25 at 12.5% per annum simple interest.

Analyze the question: The wording says "find the sum," but the options are all lengths of time. So the question is really asking for the time it takes $1,250.00 to grow to$2,031.25 at 12.5% simple interest per annum.

Concept: For simple interest,

• I = PRT/100
• Amount A = P + I

Solution:

1. Interest earned = 2,031.25 − 1,250.00 = $781.25

2. Substitute into I = PRT/100:

781.25 = (1,250 × 12.5 × T) / 100

3. Simplify the right side:

(1,250 × 12.5) / 100 = 15,625 / 100 = 156.25

So 781.25 = 156.25 × T

4. Solve for T:

T = 781.25 / 156.25 = 5 years

Check: Yearly interest = 156.25. Over 5 years, 156.25 × 5 = 781.25. Then 1,250 + 781.25 = 2,031.25 ✓

Answer: D (5 years)

Tip: When the options don't match the wording of the question, look at what the options are (years, naira, percent) to see which quantity is really being asked for. Also, always find the interest first by subtracting the principal from the amount: I = A − P.