The simple interest formula I = Prt tells you the interest. Most of the time, though, the number you actually need is the total: what a borrower will owe on the due date, or what an investment will be worth when it matures. That total is A = P(1 + rt). This calculator finds it, works backward to the principal, rate or time, and shows how far simple growth falls behind compounding.
How to use the calculator
- Pick what to solve for: the total amount (A), principal (P), rate (r) or time (t).
- Enter the other three values. Time may be in years, months or days; for days, choose a 365- or 360-day year.
- Read the result, the interest earned or owed, and the growth factor (1 + rt).
- Compare the simple total with a yearly-compounded total in the chart and table.
The formula and its rearrangements
A is the total, P the principal, r the annual rate as a decimal and t the time in years. The interest is always I = A − P.
Worked examples
Total: $5,000 at 4% for 6 years → A = 5,000 × (1 + 0.04 × 6) = 5,000 × 1.24 = $6,200; interest $1,200.
Principal: to have $6,200 in 6 years at 4% → P = 6,200 ÷ 1.24 = $5,000.
Rate: $5,000 grows to $6,200 in 6 years → r = (1.24 − 1) ÷ 6 = 0.04 = 4%.
Time: $5,000 at 4% reaches $6,200 → t = 0.24 ÷ 0.04 = 6 years.
A shorter example: borrowing $5,000 for 18 months at 4% simple interest means repaying 5,000 × (1 + 0.04 × 1.5) = $5,300 on the due date.
Simple growth vs. compound growth
The table shows the same $5,000 at 4% under both methods:
| Year | Simple interest | Compounded yearly | Difference |
|---|---|---|---|
| 1 | $5,200.00 | $5,200.00 | $0.00 |
| 2 | $5,400.00 | $5,408.00 | $8.00 |
| 4 | $5,800.00 | $5,849.29 | $49.29 |
| 6 | $6,200.00 | $6,326.60 | $126.60 |
Simple interest adds the same $200 every year, so it plots as a straight line. Compounding adds interest on interest, so the curve bends upward. In the first year the two are identical; the gap grows with time and with the rate.
Where A = P(1 + rt) is used
Promissory notes and short-term loans
Business notes, private loans and bridge loans often state a simple rate and a due date. The maturity value is the amount the borrower must pay back.
Bonds and Treasury instruments
Bond coupons pay simple interest on the face value, and accrued interest between coupon dates is calculated on a simple basis. Treasury bills are sold at a discount and pay the face value at maturity.
Comparing with a compound rate
If you are offered a simple rate on one product and a compounded rate on another, put both on the same footing. A simple 4% over 6 years is equivalent to about 3.65% compounded yearly, since (1.24)1/6 − 1 ≈ 0.0365.
For the interest alone, use the simple interest calculator; for accounts that pay interest on interest, use the compound interest calculator.
Results are estimates. Day-count rules and rounding in your agreement determine the exact amount due.
Frequently asked questions
What does A = P(1 + rt) mean?
A is the accumulated amount — principal plus simple interest — after t years at annual rate r on principal P. It comes from adding the simple interest I = Prt to the principal: A = P + Prt = P(1 + rt).
How do I find the principal from the total?
Divide the total by the growth factor: P = A ÷ (1 + rt). To have $6,200 in 6 years at 4% simple interest, you need 6,200 ÷ 1.24 = $5,000 today.
How is the maturity value of a note calculated?
A note's maturity value is its face amount plus simple interest to the due date, which is exactly A = P(1 + rt). A $5,000 note at 4% due in 18 months has a maturity value of 5,000 × (1 + 0.04 × 1.5) = $5,300.
Why does compounding give a larger total?
With compounding, each year's interest is added to the balance and earns interest itself. Over 6 years at 4%, $5,000 grows to $6,200 with simple interest but $6,326.60 compounded yearly — a gap that widens every year.