Simple Interest
Find the interest and final balance on a principal that earns a flat annual rate.
Total after 3 yr: $1,150.00
Simple interest is I = P × r × t, where r is the annual rate as a decimal and t is time in years. So $1,000 at 5% for 3 years earns 1,000 × 0.05 × 3 = $150 in interest, for a total of $1,150. Only the original principal earns interest — never the interest itself.
What simple interest is
Simple interest is charged or earned on the original principal only. Each period adds the same fixed amount, so the balance grows in a straight line. That makes it easy to predict: triple the time and you triple the interest. The flip side is that, unlike compound interest, your earned interest never starts earning interest of its own.
P = principal · r = annual rate as a decimal · t = time in years · total A = P + I
Worked example
You deposit $1,000 in an account paying 5% simple interest per year and leave it for 3 years.
- 1 Write down the inputs. Principal P = $1,000, annual rate 5%, time t = 3 years.
- 2 Convert the rate to a decimal. 5% ÷ 100 = 0.05.
- 3 Multiply P × r × t. 1,000 × 0.05 × 3 = $150 of interest.
- 4 Add the interest to the principal. $1,000 + $150 = $1,150 total.
Simple vs. compound interest over time
$1,000 at 5% per year — simple interest is flat each year, compound interest builds on the new balance (annual compounding).
| Year | Simple — balance | Compound — balance | Difference |
|---|---|---|---|
| 1 | $1,050.00 | $1,050.00 | $0.00 |
| 3 | $1,150.00 | $1,157.63 | $7.63 |
| 5 | $1,250.00 | $1,276.28 | $26.28 |
| 10 | $1,500.00 | $1,628.89 | $128.89 |
| 20 | $2,000.00 | $2,653.30 | $653.30 |
When simple interest applies
Because the interest never compounds, simple interest grows linearly while compound interest grows exponentially — and the gap widens the longer the money sits, as the table shows. Over short terms the two are nearly identical, but over decades compound interest pulls far ahead.
You will most often see simple interest on some short-term and car loans, certain bonds that pay a fixed coupon on face value, and many back-of-the-envelope estimates. Most savings accounts, credit cards, and mortgages use compound interest instead, so always check which method a product actually uses before comparing rates.