The CD maturity formula
A certificate of deposit grows by compound interest. With a rate compounded n times a year, the per-period rate is i = rate ÷ n and the number of periods is n × (months ÷ 12). The value at maturity is:
maturity = deposit × (1 + i)periods
APY = ( (1 + i)n − 1 ) × 100
The interest earned is simply the maturity value minus your deposit. The APY (annual percentage yield) restates the nominal rate as a true annual return once compounding is included — it's the figure US banks must quote and the one to compare across CDs.
Worked example
A $10,000 deposit at 4.5% compounded monthly for 12 months:
Per-period rate: 4.5% ÷ 12 = 0.375% (i = 0.00375).
Periods: 12 × (12 ÷ 12) = 12.
Maturity value: 10,000 × (1.00375)12 = $10,459.40.
Interest earned: $10,459.40 − $10,000 = $459.40.
Effective APY: (1.0037512 − 1) × 100 = 4.594%.
How compounding changes the APY
For the same 4.5% nominal rate, compounding more often nudges the APY up — but only by tiny amounts. The term length and the headline rate drive your return far more than the compounding choice.
| Compounding | APY on 4.5% | Interest on $10,000 (12 mo) |
|---|---|---|
| Annually | 4.500% | $450.00 |
| Quarterly | 4.577% | $457.68 |
| Monthly | 4.594% | $459.40 |
| Daily | 4.602% | $460.24 |
Note: this assumes the CD is held to maturity. Cashing out early usually triggers an early-withdrawal penalty (often several months of interest), which this calculator does not subtract.