Enter a loan balance or principal and the annual interest rate (%) to calculate the quarterly interest owed on the loan.
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Quarterly Interest Formula
The calculator uses a different formula for each tab.
One quarter (simple):
I = P * q
Compounded over multiple quarters:
A = P * (1 + q)^n
Solve for rate or balance:
q = I / P P = I / q
- I = quarterly interest amount
- P = principal or starting balance
- A = ending balance after compounding
- q = quarterly rate (as a decimal)
- n = number of quarters
The quarterly rate depends on how the input rate is quoted. If you enter an annual APR, q = APR / 4. If you enter an annual APY, q = (1 + APY)^(1/4) - 1. If you enter a quarterly rate directly, q is used as is. The compound formula assumes no deposits or withdrawals during the term.
Reference Values
Use these tables to sanity-check your inputs and results.
| Annual APR | 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 6% APR, 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 = $28,159.59
- Total interest over two years: $3,159.59
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. Entering APY when the rate is APR overstates the quarterly figure, and the reverse understates 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 slightly higher than the APR.
