Simple Interest

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Interest computed only on the original principal, growing linearly with time.

Simple interest is computed as a fixed rate of the original principal for each period, with no compounding. If P is the principal, r is the annual interest rate (expressed as a decimal), and t is the time in years, then the interest earned is I = P · r · t and the final amount is A = P · (1 + r · t). Simple interest grows linearly with time — every year adds the same amount of interest.

I = P · r · t; A = P · (1 + r · t)

• $1,000 at 5% for 3 years → I = 1000 · 0.05 · 3 = $150; A = $1,150
• €500 at 4% for 2 years → I = 500 · 0.04 · 2 = €40; A = €540
• £2,000 at 6% for 6 months (0.5 years) → I = 2000 · 0.06 · 0.5 = £60

How to recognize it

• The problem explicitly states 'simple interest'
• Interest is the same each period (no compounding language)
• Rate is quoted per time unit and you multiply by elapsed time

Common mistakes

• Using the compound interest formula when simple interest is intended
• Forgetting to convert percentage rates to decimals (5% = 0.05)
• Mixing time units (rate annual, time in months without converting)

Practice guidance

Numerical Reasoning