What is simple interest?
Simple interest is paid only on the original amount, the principal. It does not earn interest on interest, so the balance grows by the same amount every period. It is used for many car loans, short-term personal loans, some bonds and certificates of deposit, and for quick estimates. This simple interest calculator finds the interest and the end balance, or works backward to the principal, the term or the rate, and shows every step.
The simple interest formula
I = P × r × t, where I is the interest, P the principal, r the interest rate and t the time. The end balance is A = P × (1 + r × t). The four tabs of the calculator turn the formula around:
- Balance: A = P × (1 + r × t)
- Principal: P = A ÷ (1 + r × t)
- Term: t = (A ÷ P − 1) ÷ r
- Rate: r = (A ÷ P − 1) ÷ t
The rate and the term must use the same unit: a yearly rate with a term in years, or a monthly rate with a term in months. The calculator converts them for you. For example, $20,000 at 3% a year for 18 months is $20,000 × 3% × 18 ÷ 12 = $900.00.
Examples
- Interest and balance: $20,000 at 3% a year for 10 years earns $20,000 × 3% × 10 = $6,000.00, for an end balance of $26,000.00.
- Principal: to have $30,000 in 10 years at 3%, you need $30,000 ÷ (1 + 3% × 10) = $23,076.92 today.
- Term: $20,000 grows to $30,000 at 3% in ($30,000 ÷ $20,000 − 1) ÷ 3% = 16.67 years.
- Rate: $20,000 that grows to $30,000 in 10 years earns ($30,000 ÷ $20,000 − 1) ÷ 10 = 5% a year.
Simple interest by rate and term
The interest on $20,000:
| Rate | 1 year | 5 years | 10 years |
|---|---|---|---|
| 2% | $400 | $2,000 | $4,000 |
| 3% | $600 | $3,000 | $6,000 |
| 5% | $1,000 | $5,000 | $10,000 |
| 8% | $1,600 | $8,000 | $16,000 |
Simple vs compound interest
With compound interest, the interest is added to the balance and earns interest too. For short terms the difference is small, but it grows every year. $20,000 at 3%, compounded annually:
| Years | Simple | Compound | Difference |
|---|---|---|---|
| 1 | $20,600.00 | $20,600.00 | $0.00 |
| 5 | $23,000.00 | $23,185.48 | $185.48 |
| 10 | $26,000.00 | $26,878.33 | $878.33 |
| 20 | $32,000.00 | $36,122.22 | $4,122.22 |
| 30 | $38,000.00 | $48,545.25 | $10,545.25 |
After 10 years compound interest gives $26,878.33 instead of $26,000.00. Savings accounts and most investments compound, so use the compound interest calculator or the interest calculator for them.
Daily simple interest on loans
Most auto loans and many personal loans charge simple interest on the balance you still owe, day by day: daily interest = balance × rate ÷ 365. On a $25,000 balance at 6%, that is $4.11 a day. A payment made 10 days late costs about $41.10 more interest, and a payment made early or an extra payment lowers the interest, because it cuts the balance sooner. The loan calculator shows the full payment schedule.
Exact and ordinary interest
For a term in days, lenders divide by 365 days (exact interest) or by 360 days (ordinary or banker's interest). $20,000 at 3% for 90 days:
| Method | Formula | Interest |
|---|---|---|
| Exact | P × r × 90 ÷ 365 | $147.95 |
| Ordinary | P × r × 90 ÷ 360 | $150.00 |
A 360-day year gives slightly more interest. To use it here, enter the term as 90 ÷ 360 × 12 = 3 months.
Where simple interest is used
- Car and personal loans: daily simple interest on the balance owed.
- Bonds: the coupon is the face value times the coupon rate, paid without compounding; see the bond calculator.
- Some CDs: CDs that pay out the interest instead of adding it to the balance; see the CD calculator.
- Short-term loans and notes: a fixed fee or rate for a few months.