Simple interest and total amount
Starting amount, yearly rate, and time. The result also shows what compound interest would give.
How simple interest works
With simple interest, each period's interest is figured on the starting amount only. Earlier interest never joins the base, so the balance grows in a straight line: the same dollar amount every year.
Example: $5,000 at 6% a year for 4 years. I = 5,000 × 0.06 × 4 = $1,200, so the total is $6,200. For a time in months, divide by 12 first: 18 months is 1.5 years.
Daily interest uses a 365-day year here. A $20,000 balance at 6% a year accrues 20,000 × 0.06 ÷ 365 = $3.29 a day. Your lender may use 360 or 365 days, so check your loan terms.
Simple interest vs compound interest
The gap grows with time. With compound interest, earlier interest earns interest of its own. With simple interest, it does not.
| Years | Simple (5% a year) | Compounded monthly (5% a year) | Difference |
|---|---|---|---|
| 1 | $1,050.00 | $1,051.16 | $1.16 |
| 5 | $1,250.00 | $1,283.36 | $33.36 |
| 10 | $1,500.00 | $1,647.01 | $147.01 |
| 20 | $2,000.00 | $2,712.64 | $712.64 |
Most savings accounts and CDs compound. Many car loans and student loans are called simple interest loans because interest builds on the unpaid principal balance each day, not on past interest. Ask your lender exactly how your loan accrues interest.
Common mistakes
- Mixing units: a yearly rate with a time in months. Convert first (18 months = 1.5 years).
- Typing the rate as a decimal: enter 6 for 6%, not 0.06.
- Mixing up interest and total: I is only the earnings, and the total includes the principal.
- Dividing a yearly rate by 12 to get a monthly rate works for simple interest, but compound interest needs a different conversion.
Frequently asked questions
What is the simple interest formula?
I = P × r × t for the interest and Total = P × (1 + r × t) for the total, with the rate as a yearly decimal and the time in years.
How do I calculate simple interest per month?
Multiply the principal by the yearly rate, then by the months divided by 12. On $5,000 at 6%, one month earns 5,000 × 0.06 × 1/12 = $25.
How do I calculate daily simple interest?
Divide the yearly rate by 365 and multiply by the balance. At 6% on $20,000, the daily interest is $3.29.
What is the difference between simple and compound interest?
Simple interest is figured on the starting amount only. Compound interest is figured on the balance plus earlier interest, so growth speeds up over time.
How do I find the interest rate with simple interest?
Use r = (Total ÷ P − 1) ÷ t. With P = $1,000, a total of $1,300, and 10 years, the rate is 3% a year.
How do I find the time with simple interest?
Use t = (Total ÷ P − 1) ÷ r. With P = $2,000, a total of $2,600, and 6% a year, the time is 5 years.
Sources and review
- Financial mathematics: simple interest and compound interest formulas.