The simple interest formula
Simple interest is calculated on the principal alone: I = P × r × t, where P is the principal, r is the annual rate as a decimal and t is the time in years. $10,000 at 5% for three years earns 10,000 × 0.05 × 3 = $1,500, and the total repaid or received is $11,500. Because interest never earns interest, the amount is the same every year: $500, $500, $500.
Rearranged, the same formula gives any missing piece: P = I ÷ (r × t), r = I ÷ (P × t), t = I ÷ (P × r). The Solve-for tabs do the rearranging; enter the three you know.
- Interest: I = P × r × t
- Principal: P = I ÷ (r × t)
- Rate: r = I ÷ (P × t)
- Time: t = I ÷ (P × r)
- Total amount: A = P + I = P(1 + rt)
Simple versus compound interest
Under compound interest, each period's interest is added to the balance and earns interest itself. For short periods the two are close; over long ones they diverge sharply. At 5%, simple interest on $10,000 over 30 years is $15,000; compounded monthly it is nearly $35,000. Savings accounts, bonds' reinvested coupons, and most long-term investments compound. Simple interest survives mainly in short-term and consumer contexts: some auto and personal loans, short-term notes, late-payment charges, and the daily interest accrual between payments on many loans.
| Time | Simple interest | Compounded yearly | Compounded monthly |
|---|---|---|---|
| 1 years | $500.00 | $500.00 | $511.62 |
| 2 years | $1,000.00 | $1,025.00 | $1,049.41 |
| 5 years | $2,500.00 | $2,762.82 | $2,833.59 |
| 10 years | $5,000.00 | $6,288.95 | $6,470.09 |
| 20 years | $10,000.00 | $16,532.98 | $17,126.40 |
| 30 years | $15,000.00 | $33,219.42 | $34,677.44 |
Interest at different rates
Because simple interest is linear, doubling the rate doubles the interest and doubling the time doubles it again. The table gives $10,000 over one, three and five years.
| Rate | 1 year | 3 years | 5 years |
|---|---|---|---|
| 2% | $200.00 | $600.00 | $1,000.00 |
| 4% | $400.00 | $1,200.00 | $2,000.00 |
| 5% | $500.00 | $1,500.00 | $2,500.00 |
| 6% | $600.00 | $1,800.00 | $3,000.00 |
| 8% | $800.00 | $2,400.00 | $4,000.00 |
| 10% | $1,000.00 | $3,000.00 | $5,000.00 |
| 12% | $1,200.00 | $3,600.00 | $6,000.00 |
Interest per day
Loans quoted with simple daily interest accrue P × r ÷ 365 each day. This is the figure on a payoff quote (the per-diem) and the reason paying a few days early or late changes the amount by a few dollars. The calculator reports the daily and monthly amounts for whatever you enter.
| Principal | Per day | Per month | Per year |
|---|---|---|---|
| $1,000 | $0.14 | $4.17 | $50.00 |
| $5,000 | $0.68 | $20.83 | $250.00 |
| $10,000 | $1.37 | $41.67 | $500.00 |
| $25,000 | $3.42 | $104.17 | $1,250.00 |
| $100,000 | $13.70 | $416.67 | $5,000.00 |
Simple-interest loans and how they differ from amortized loans
A loan described as 'simple interest' usually means interest accrues daily on the outstanding balance, and each payment first covers accrued interest, then reduces principal. That is exactly how an amortized loan works too; the label mostly distinguishes it from 'precomputed' or add-on loans, where the total interest is fixed at the start with I = Prt and divided into equal payments regardless of when you pay. Add-on loans cost more for the same quoted rate because you keep paying interest on principal you have already repaid. The table compares the two on a $20,000 car loan at 7%.
| Term | Add-on interest | Total repaid | Add-on monthly payment | Amortized monthly payment |
|---|---|---|---|---|
| 2 years | $2,800.00 | $22,800.00 | $950.00 | $895.45 |
| 3 years | $4,200.00 | $24,200.00 | $672.22 | $617.54 |
| 4 years | $5,600.00 | $25,600.00 | $533.33 | $478.92 |
| 5 years | $7,000.00 | $27,000.00 | $450.00 | $396.02 |
When to use this calculator
Use it for anything where interest is charged or paid on the original amount only: a short-term personal loan between individuals, a treasury bill or commercial paper held to maturity, a late fee or statutory interest on an unpaid invoice, a bond's coupon payments taken as cash, or the interest between two dates on a fixed balance. For savings, mortgages and investments, use the compound interest, mortgage or investment calculators.