Simple Interest
What this domain tests
Simple interest is charged only on the original principal, so the balance grows linearly. Expect items that compute interest or maturity value, and items that work backwards to find principal, rate, or time.
Core rules
- Formula: I = P × r × t, where P is principal, r is the annual rate written as a decimal, and t is time in years.
- Time conversion: months ÷ 12; days ÷ 360 for ordinary (banker's) interest or ÷ 365 for exact interest. Ordinary interest produces the larger figure.
- Maturity value: A = P + I = P(1 + rt).
- Solving for an unknown: P = I ÷ (rt); r = I ÷ (Pt); t = I ÷ (Pr).
- Convert quoted rates before substituting: 7.5% = 0.075.
- Bank discount: the bank deducts interest from the face value in advance, so proceeds = face value − discount, and the effective rate is higher than the stated discount rate.
Worked example
A retailer borrows $4,800 at 7.5% simple interest for 9 months. What is the maturity value? t = 9 ÷ 12 = 0.75 year. I = 4,800 × 0.075 × 0.75 = 4,800 × 0.05625 = $270. A = 4,800 + 270 = $5,070.
Traps that cost marks
- Entering 9 (months) as t instead of 0.75 year, which inflates interest twelvefold.
- Using 365 days when the problem specifies a 360-day year, or the reverse.
- Computing interest on the maturity value rather than on the principal.
- Forgetting to add principal back when the question asks for the amount repaid.
- Using a percent figure directly (7.5 instead of 0.075).
Where it appears
Notes discounted at a bank, short-term working-capital loans, and simple-interest installment contracts all follow this formula, so the same reasoning transfers directly to those word problems.