Simple Interest Formula
Simple interest is calculated using a straightforward formula:
I = P × r × t
- I = total interest earned or paid
- P = principal (initial amount)
- r = annual interest rate (as a decimal)
- t = time in years
The end balance (total amount) is: A = P + I = P(1 + rt)
Solving for Each Variable
- End Balance: A = P(1 + rt)
- Principal: P = A / (1 + rt)
- Rate: r = (A - P) / (Pt)
- Term: t = (A - P) / (Pr)
Simple vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Calculation base | Original principal only | Principal + accumulated interest |
| Growth pattern | Linear | Exponential |
| Annual interest | Same every year | Increases each year |
| Common uses | Auto loans, T-bills, short-term loans | Savings accounts, mortgages, credit cards |
Example
You invest $15,000 at 4.5% simple interest for 8 years:
- Annual interest = $15,000 × 4.5% = $675
- Total interest = $675 × 8 = $5,400
- End balance = $15,000 + $5,400 = $20,400
With compound interest at the same rate, the end balance would be $21,781 — showing how compounding accelerates growth over longer periods.
When Simple Interest Applies
- Auto loans: Many car loans use simple interest calculated on the remaining principal
- Short-term loans: Payday loans and bridge loans often use simple interest
- Treasury bills: U.S. T-bills and some government bonds use simple interest
- Student loans: Federal student loans accrue simple interest on the principal balance
- Certificates of Deposit: Some CDs pay simple interest rather than compound