The simple interest formula
I = P × r × t A = P + I
Where P is the principal, r is the annual interest rate as a decimal (5% = 0.05), t is the time in years and A is the total amount at the end. Months are converted to years by dividing by 12, so 18 months is 1.5 years.
For example, $10,000 at 5% for 3 years earns 10,000 × 0.05 × 3 = $1,500 in interest, for a total of $11,500.
How to calculate simple interest by hand
Say you lend a friend $8,000 at 4.5% a year and they repay everything after 2 years and 6 months.
- Write the rate as a decimal: 4.5% ÷ 100 = 0.045.
- Convert the time to years: 2 years and 6 months = 2 + 6 ÷ 12 = 2.5 years.
- Multiply principal, rate and time: 8,000 × 0.045 × 2.5 = $900 of interest.
- Add the interest to the principal for the amount owed: 8,000 + 900 = $8,900.
To find the interest for a single year, skip the time step: 8,000 × 0.045 = $360. Simple interest is the same $360 in every year of the term, which makes it easy to check a statement line by line.
Simple vs compound interest
Simple interest is charged only on the original principal, so it grows by the same amount every year. Compound interest is charged on the principal plus interest already earned, so it grows faster over time. At the same rate and term, compound interest always ends up higher once more than one compounding period has passed.
| Years | Simple interest | Compounded yearly | Compounded monthly |
|---|---|---|---|
| 1 | $10,500.00 | $10,500.00 | $10,511.62 |
| 5 | $12,500.00 | $12,762.82 | $12,833.59 |
| 10 | $15,000.00 | $16,288.95 | $16,470.09 |
| 20 | $20,000.00 | $26,532.98 | $27,126.40 |
- Simple interest is common for some car loans, short-term personal loans and certain bonds.
- Savings accounts and most investments compound, so use a compound interest calculator for those.
Common mistakes
- Entering the rate as a whole number. In the formula, 6% is 0.06, not 6. The calculator handles this for you, but hand calculations often go wrong here.
- Mixing months and years. A monthly rate needs time in months; an annual rate needs time in years. Don't multiply an annual rate by a number of months.
- Assuming a loan uses simple interest. Credit cards and most mortgages charge interest on the outstanding balance, which behaves differently. Check your loan agreement before relying on the result.