Simple Interest Formula
I = P × r × t A = P + I
Where I is interest, P is principal, r is the annual rate (as decimal), and t is time in years. Simple interest does not compound: you earn the same amount of interest each period.
Time must be in years because the rate is a yearly rate. Six months is t = 0.5. For days, divide by the number of days in the year the lender uses: 90 days is 90/365 = 0.2466 on a 365-day basis, or 90/360 = 0.25 on a 360-day basis.
The same formula rearranges to find any missing value. That is what the "Solve for" switch above does:
- Principal: P = I ÷ (r × t)
- Rate: r = I ÷ (P × t)
- Time: t = I ÷ (P × r)
A worked example
You lend $5,000 at 5% a year for 3 years. The interest is 5,000 × 0.05 × 3 = $750, so you get back $5,750. That is $250 a year, about $20.83 a month and $0.68 a day.
The same $5,000 at 5% compounded monthly grows to 5,000 × (1 + 0.05/12)36 = $5,807.36. The extra $57.36 is interest earned on interest. Over 3 years the gap is small. Over 30 years it is large: simple interest gives $12,500, monthly compounding gives $22,339.
Working backwards: if you want $750 of interest from $5,000 in 3 years, you need r = 750 ÷ (5,000 × 3) = 0.05, which is 5%. At 4% it would take t = 750 ÷ (5,000 × 0.04) = 3.75 years.
Where simple interest is used
Auto loans in the US. Most car loans are simple-interest loans. Interest accrues each day on the principal you still owe, at the APR divided by 365. On a $25,000 balance at 7% that is about $4.79 a day. Your payment covers the interest built up since the last payment and the rest cuts the principal. Paying a few days early saves a little interest. Paying late costs a little more. Our auto loan calculator shows the full schedule.
Treasury bills. T-bills pay no coupon. You buy them below face value and get the full face value at maturity. The price comes from a simple discount rate on a 360-day year. A $1,000 bill with 182 days to run at a 4% discount rate costs 1,000 × (1 − 0.04 × 182/360) = $979.78.
Some personal loans and short-term credit. Many personal loans, payday-style loans, and loans between family members quote a flat or simple rate. Be careful with "flat rate" loans that charge interest on the original amount for the whole term even as you repay it. Their true APR is close to double the quoted rate.
Certificates of deposit and bonds often pay simple interest per period (a bond's coupon is simple interest on face value), but if you reinvest the payments your overall return compounds.
365 or 360 days?
Lenders do not all count a year the same way. Consumer loans in the US usually use actual/365. Many commercial loans, money market instruments and T-bills use actual/360, which divides by 360 but counts the real number of days. That quietly raises the cost. On $10,000 at 6% for 90 days, a 365-day basis gives $147.95 of interest and a 360-day basis gives $150.00. Over a full year of 365 days the 360 basis charges 6.08% instead of 6%.
Simple vs compound interest
With simple interest, interest is always worked out on the original principal. With compound interest, interest is added to the balance and then earns interest itself. For a borrower, simple interest is cheaper. For a saver, compound interest pays more. For short periods the two are almost the same, which is why simple interest is common for loans and deposits under a year. See the compound interest calculator for regular deposits and different compounding frequencies.