Simple Interest Formula With Examples
Simple interest is I = P × r × t. Enter $2,000 at 5% for 4 years and you get $400 of interest and $2,400 in total, with no interest charged on interest.
The simple interest formula is I = P × r × t, which is the principal times the annual rate times the time in years. $2,000 at 5% for 4 years earns $400, and because that interest never earns interest of its own, simple interest and non-compound interest are the same thing.
Add the interest to the principal for the total, A = P + I. In this example that's $2,400. Every rate in this article is an example for the arithmetic, not a quote.
What goes into the formula
P is the principal, the amount borrowed or deposited. The rate r is the annual rate as a decimal, so 5% is 0.05. The time t is in years, because the rate is a rate per year.
So a shorter term still has to go in as years, which means dividing months by 12 and days by 365. Some contracts divide by 360 instead, and the guide to accrued interest shows what that does to the bill.
The same $2,000 over three terms
Four years. 2,000 × 0.05 × 4 = $400.00 of interest, for a total of $2,400.00.
Nine months. The time is 9 ÷ 12 = 0.75 years. 2,000 × 0.05 × 0.75 = $75.00, for a total of $2,075.00.
120 days. The time is 120 ÷ 365 years. 2,000 × 0.05 × 120 ÷ 365 = $32.88, for a total of $2,032.88. Divide last. If you round the time to 0.33 first, you get $33.00, which is 12 cents too much.
The simple interest calculator returns all three. Enter 2000 and 5, then the time, and set the unit to years, months or days. For 120 days it also shows the basis it used, "120 days, counted as 120/365 of a year."
Working the formula backward
When you know the interest and need one of the other values, rearrange the formula. The calculator only solves for the interest, so run these by hand and then enter the answer to check it.
| You need | Formula | Example | Answer |
|---|---|---|---|
| The rate | r = I ÷ (P × t) | A $6,000 loan costs $540 over 2 years | 540 ÷ (6,000 × 2) = 0.045, or 4.5% |
| The time | t = I ÷ (P × r) | $6,000 at 4.5% has to earn $810 | 810 ÷ (6,000 × 0.045) = 3 years |
| The principal | P = I ÷ (r × t) | $144 of interest at 8% over 18 months | 144 ÷ (0.08 × 1.5) = $1,200 |
Simple versus compound over the same term
Compound interest adds each period's interest to the balance, so the next period charges interest on a larger amount. Here is the interest on $8,000 at 7%, with nothing added or repaid along the way.
| Term | Simple interest | Compounded annually | Compounded monthly |
|---|---|---|---|
| 1 year | $560.00 | $560.00 | $578.32 |
| 5 years | $2,800.00 | $3,220.41 | $3,341.00 |
| 10 years | $5,600.00 | $7,737.21 | $8,077.29 |
| 20 years | $11,200.00 | $22,957.48 | $24,309.91 |
At one year, simple interest and annual compounding match, because no interest has been added to the balance yet. Monthly compounding is already ahead by $18.32. By 20 years, annual compounding has paid more than twice the simple figure, a gap of $11,757.48.
The direction of that gap decides which side you want. On a debt, you'd rather pay simple interest. On savings, you'd rather earn compound interest. To reproduce the compound columns, enter 8000, 7 and the years in the compound interest calculator, pick the frequency and leave the monthly contribution at 0.
Where simple interest is used
Auto loans. Chase's page on simple interest auto loans multiplies the outstanding principal by a daily rate, the annual rate divided by 365, and applies payments to the outstanding interest first. On a $20,000 balance at 7%, 30 days comes to 20,000 × 0.07 × 30 ÷ 365 = $115.07.
Federal student loans. MOHELA, a federal student loan servicer, gives a daily formula of balance times rate divided by the days in the year. Its example, $25,000 at 6.8% divided by 365.25, comes to $4.65 a day. The calculator divides by 365, so one day on the same balance shows $4.66. Unpaid student loan interest can later join the principal, which the student loan article works through.
Bonds with a fixed coupon. FINRA's bond glossary defines a coupon as the interest payment on a bond and gives the example of a $1,000 bond paying $65 a year, a 6.5% coupon rate. Each payment is figured on the face value, so ten years of coupons come to 1,000 × 0.065 × 10 = $650.00.
A savings account behaves differently once the bank credits interest to your balance. The accrued interest guide explains how accrual turns into compounding.
When P × r × t overstates a loan
The formula assumes the principal stays put for the whole term. A loan with monthly payments breaks that assumption, because every payment lowers the balance the next month's interest is charged on.
Take $20,000 at 7% for 5 years. P × r × t says $7,000.00. Repaid in level monthly payments, the same loan costs $3,761.48 in interest, a little over half as much. Use the loan calculator for that kind of loan and keep the simple interest formula for one payment period at a time, or for a sum repaid all at once at the end.