Work out simple interest from the original principal, the rate, and the term — or flip the formula and solve for the starting amount, how long it takes, or the rate. Simple interest never compounds: every period's interest is calculated on the same starting balance.
Simple vs. compound interest
| $10,000 at 5% for 5 years | |
|---|---|
| Simple interest | $12,500 ($2,500 of interest) |
| Compounded monthly | about $12,833.59 ($2,833.59 of interest) |
Examples
$20,000 at 3% for 10 years
A $20,000 principal at 3% simple interest for 10 years earns $6,000 of interest, so the end balance is $26,000. Each year adds a flat $600.
What principal grows to $30,000?
To reach $30,000 in 10 years at 3% simple interest you need a starting principal of $23,076.92. The $6,923.08 of interest is 3% of that principal each year.
18 months at 3% per year
The same $20,000 at 3% for 18 months is a year and a half, so interest is $20,000 × 3% × 18 / 12 = $900 and the end balance is $20,900.
Formula
Interest is a percentage of the original principal, applied for each unit of time. With principal P, annual rate r, and term t in years:
I = P × r × t
A = P + I = P × (1 + r × t)
A monthly quoted rate is r = monthlyRate × 12. A term in months is
t = months / 12. Rearranged, the same identity gives the other tabs:
P = A / (1 + r × t)
t = (A / P − 1) / r
r = (A / P − 1) / t
Assumptions and limits
Use this equation only when the contract calculates interest on the original principal. Actual loan disclosures may use daily simple interest, add fees, or apply payments on exact dates, which this evenly spaced schedule does not model. Compare the result with the lender's written rate, APR, finance charge, and payment schedule.