Calculate yearly interest from a balance and annual rate using simple, APY or compounded rates, or solve for the rate or balance you need.
Yearly Interest Formula
The four solve modes use the formulas below. Rates are decimals in the equations; the input accepts either percent or decimal notation.
Balance + rate (simple):
Balance + rate (compounded during the year):
Periodic amount:
Find balance or rate:
For the compound reverse-rate solve, g is the nth root of (1 + f).
- I = yearly interest
- B = principal balance
- r = nominal annual decimal rate in compound mode; otherwise the simple annual rate or APY (5% = 0.05)
- f = effective one-year interest factor; f = r for simple/APY mode. The reverse r equation applies to compound mode.
- n = compounding periods per year
- p = interest paid per period
- k = number of periods per year
The balance is held constant for one year. No deposits, withdrawals, fees, or taxes are factored in. Use the simple formula when your rate is already an APY or a flat annual rate. Use the compound formula for a nominal annual interest rate with the matching frequency, assuming earned interest remains in the account. A fee-inclusive loan APR may differ from that nominal rate. Monthly and daily results are arithmetic averages, not promised payout amounts.
Reference Tables
Yearly interest on a $10,000 balance at common annual rates, simple calculation:
| Annual rate | Yearly interest | Monthly |
|---|---|---|
| 0.5% | $50 | $4.17 |
| 2% | $200 | $16.67 |
| 4% | $400 | $33.33 |
| 5% | $500 | $41.67 |
| 7% | $700 | $58.33 |
| 10% | $1,000 | $83.33 |
How an APR turns into an effective yearly rate at different compounding frequencies:
| APR | Monthly | Daily |
|---|---|---|
| 3% | 3.04% | 3.05% |
| 6% | 6.17% | 6.18% |
| 12% | 12.68% | 12.75% |
| 20% | 21.94% | 22.13% |
Worked Example
You have $25,000 in an account paying 4.5% APR compounded monthly. Using the compound formula:
I = 25,000 × ((1 + 0.045/12)12 - 1) = 25,000 × 0.04594 = $1,148.50
If the same account quoted 4.5% APY instead, the yearly interest would be a flat 25,000 × 0.045 = $1,125.
FAQ
Should I enter APR or APY? An APY already includes compounding: use the simple/APY option for the one-year calculation. For compound mode, use the nominal annual interest rate and the stated compounding frequency. Check the account terms; a fee-inclusive borrowing APR is not necessarily the nominal interest rate.
Why is my compound result higher than the simple result? Compounding pays interest on prior interest within the year. The more frequent the compounding, the larger the gap.
Does this work for loan interest? It can illustrate interest under a constant-balance model using a nominal rate. It does not model fees, daily changing balances, payment timing or principal paydown on amortizing loans.
Can I find the rate from interest paid? Yes. Choose the annual-rate solve mode and enter both numbers. Compound mode returns the nominal rate for your selected frequency; simple/APY mode returns the one-year effective rate.
