Simple Interest: Formula, Worked Examples and How It Differs from Compound Interest

With simple interest the rate always applies to the original amount, so interest grows in a straight line: every month (or year) earns exactly the same. It is a favourite of school and exam questions – and understanding it well shows why compound interest is so powerful.

The formula

I = P × r × t and A = P + I = P × (1 + r × t)

• I – interest;
• P – principal (the starting amount);
• r – rate per period, as a decimal (2% = 0.02);
• t – time, in the same unit as the rate;
• A – final amount (principal + interest).

The golden rule: rate and time must use the same unit. A monthly rate needs the time in months; a yearly rate, in years. With simple interest the conversion is proportional: 24% a year equals 2% a month. Under the commercial convention a month has 30 days and a year 360.

Worked examples

1. Interest and final amount

R$ 1,000 at 2% a month for 10 months: I = 1,000 × 0.02 × 10 = R$ 200, and A = R$ 1,200.

2. Finding the rate

R$ 2,000 became R$ 2,600 in 12 months. The interest was R$ 600, so r = I ÷ (P × t) = 600 ÷ (2,000 × 12) = 0.025 = 2.5% a month.

3. Finding the time

How long does R$ 5,000 at 1.5% a month take to earn R$ 900? t = I ÷ (P × r) = 900 ÷ (5,000 × 0.015) = 12 months.

4. Finding the principal

What amount, at 2% a month for 5 months, grows to R$ 3,300? P = A ÷ (1 + r × t) = 3,300 ÷ 1.10 = R$ 3,000.

5. A term in days

R$ 4,000 at 3% a month for 45 days: 45 days are 1.5 months, so I = 4,000 × 0.03 × 1.5 = R$ 180.