Calculate quarterly compound interest: enter principal, annual rate and time to get the ending balance and interest, or solve for principal, rate or time.
Quarterly Interest Formula
The four solve modes rearrange the same constant-rate compound model. No deposits, withdrawals, fees or taxes are included; fractional quarters use exponential interpolation.
One quarter (simple):
Compounded over multiple quarters:
Solve for principal, rate or time:
- I = quarterly interest amount
- P = principal or starting balance
- A = ending balance after compounding
- q = quarterly rate (as a decimal)
- n = number of quarters
Convert percentage rates to decimals first. A nominal annual decimal rate r gives q = r / 4. An annual APY decimal y gives q = (1 + y)(1/4) - 1 in this equal-quarter model. A quarterly decimal rate is q directly. The quarterly growth factor must be positive. Inverse rate and time solves require positive balances; rate solving requires positive time, and zero rate cannot determine a unique time. A consumer loan APR may include fees and is not the fee-free nominal rate modeled here. Actual bank day-count and settlement rules can differ.
Reference Values
Use these tables to sanity-check your inputs and results.
| Nominal annual rate | Quarterly rate | Effective APY | Interest on $10,000 / quarter |
|---|---|---|---|
| 1% | 0.2500% | 1.0038% | $25.00 |
| 3% | 0.7500% | 3.0339% | $75.00 |
| 5% | 1.2500% | 5.0945% | $125.00 |
| 7% | 1.7500% | 7.1859% | $175.00 |
| 10% | 2.5000% | 10.3813% | $250.00 |
| Where the rate appears | Usually quoted as |
|---|---|
| Savings, CDs, money market | APY |
| Mortgages, auto loans, personal loans | APR |
| Credit cards | APR (with daily compounding) |
| Bonds, treasury notes | Annual coupon rate |
| Corporate finance, lease accounting | Quarterly rate or APR |
Worked Example
You hold $25,000 in an account paying a 6% nominal annual rate, compounded quarterly. You want to know the interest earned in one quarter and the balance after two years.
- Quarterly rate: q = 6% / 4 = 1.5%
- One quarter of interest: I = 25,000 * 0.015 = $375.00
- Two years = 8 quarters, so A = 25,000 * (1.015)8 = $28,162.31
- Total interest over two years: $3,162.31
If APR and APY produce different results, which should you use? Match the input to how the rate is published. A bank advertising 4.00% APY is not the same as 4.00% APR. For positive rates, interpreting a nominal annual quote as APY understates the quarterly rate; interpreting an APY quote as nominal annual rate overstates it.
Why does the four-quarter total differ from APY interest? Multiplying one quarter of simple interest by four ignores compounding. The APY figure includes interest earned on prior quarters' interest, which is why it is higher than the positive nominal annual rate under this quarterly model.
