The CD Interest Formula
A certificate of deposit grows with compound interest, so the amount you have at maturity depends on three things: how much you deposit, the rate, and how long the money stays in. Which formula you use depends on the kind of rate you have.
If you have the APY (annual percentage yield, the rate banks advertise):
A = P × (1 + APY)t
If you have a nominal interest rate and its compounding frequency:
A = P × (1 + r/n)n×t
- A = maturity value (deposit plus interest)
- P = principal, the amount you deposit
- APY or r = the annual rate as a decimal (4.50% = 0.045)
- n = compounding periods per year (365 for daily, 12 for monthly, 4 for quarterly)
- t = term in years (an 18-month CD is t = 1.5)
The interest you earn is simply A − P. The two formulas give the same answer when the APY is the one that matches the nominal rate. The most common mistake is plugging an APY into the second formula: the APY already includes compounding, so compounding it again overstates your interest.
Example 1: CD Interest From an APY
Most savers start here, because U.S. banks must quote the APY under the Truth in Savings Act. Say you put $10,000 in a 12-month CD at 4.50% APY:
A = 10,000 × (1 + 0.045)1
A = $10,450.00
Interest = $10,450.00 − $10,000 = $450.00
For a one-year CD the interest is just the deposit times the APY. For other terms, use t in years. An 18-month CD at the same APY:
A = 10,000 × (1.045)1.5
A = 10,000 × 1.068254
A = $10,682.54, so interest = $682.54
Here is the same 4.50% APY across common CD terms on a $10,000 deposit:
| Term | t (years) | Interest earned | Maturity value |
|---|---|---|---|
| 3 months | 0.25 | $110.65 | $10,110.65 |
| 6 months | 0.5 | $222.52 | $10,222.52 |
| 12 months | 1 | $450.00 | $10,450.00 |
| 18 months | 1.5 | $682.54 | $10,682.54 |
| 2 years | 2 | $920.25 | $10,920.25 |
| 3 years | 3 | $1,411.66 | $11,411.66 |
| 5 years | 5 | $2,461.82 | $12,461.82 |
Example 2: Interest Compounded Quarterly, Monthly or Daily
Textbook problems, and some bank disclosures, give a nominal rate plus a compounding frequency instead of an APY. Then use A = P(1 + r/n)nt.
Quarterly: $10,000 for 2 years at 7.5% compounded quarterly
r/n = 0.075 / 4 = 0.01875 and n×t = 4 × 2 = 8
A = 10,000 × (1.01875)8 = 10,000 × 1.160222
A = $11,602.22, so the CD earns $1,602.22 in interest
Monthly: $5,000 for 3 years at 4% compounded monthly
r/n = 0.04 / 12 = 0.003333 and n×t = 12 × 3 = 36
A = 5,000 × (1.003333)36 = 5,000 × 1.127272
A = $5,636.36, so interest = $636.36
Daily: $10,000 for 1 year at 4.75% compounded daily
r/n = 0.0475 / 365 = 0.00013014 and n×t = 365
A = 10,000 × (1.00013014)365 = 10,000 × 1.048643
A = $10,486.43, so interest = $486.43
Daily compounding turned a 4.75% rate into an effective yield of 4.864%. That effective yield is exactly what the APY reports, which is why comparing APYs is the fair way to compare CDs.
Example 3: Continuous Compounding (A = Pe^rt)
Continuous compounding is the limit of compounding more and more often. It is rare on real CDs but common in finance classes:
A = P × er×t
where e ≈ 2.71828. Suppose you deposit $2,000 in a CD earning 4% compounded continuously. What is it worth in 15 years?
r×t = 0.04 × 15 = 0.6
A = 2,000 × e0.6 = 2,000 × 1.822119
A = $3,644.24, of which $1,644.24 is interest
Continuous compounding adds very little over daily compounding: at 4%, the effective yield is 4.081% versus 4.081% with daily compounding.
Check Your Numbers With the CD Calculator
Enter your deposit, rate and term. If your rate is an APY, leave Compounding on “None”. To check Example 2, choose Quarterly, enter 7.5% and 24 months.
Banks advertise an APY, which already includes compounding. Choose a frequency only if you have a nominal interest rate.
Converting Between APY and the Interest Rate
The APY is the nominal rate after a year of compounding:
APY = (1 + r/n)n − 1
And to go back from an APY to the nominal rate for a given frequency:
r = n × [(1 + APY)1/n − 1]
How a 4.50% nominal rate turns into an APY, and what it earns on $10,000 in a year:
| Compounding | Periods per year | APY | Interest on $10,000 |
|---|---|---|---|
| Annually | n = 1 | 4.500% | $450.00 |
| Semiannually | n = 2 | 4.551% | $455.06 |
| Quarterly | n = 4 | 4.577% | $457.65 |
| Monthly | n = 12 | 4.594% | $459.40 |
| Daily | n = 365 | 4.602% | $460.25 |
| Continuously | er − 1 | 4.603% | $460.28 |
Going the other way, a CD advertised at 4.50% APY that compounds monthly has a nominal rate of 4.410%; with daily compounding it is 4.402%. The yield you receive is 4.50% either way.
How Much Interest Does a CD Pay per Month?
Divide the total interest by the number of months for the average: $450.00 ÷ 12 = $37.50 a month on $10,000 at 4.50% APY. If the bank pays the interest out to you every month instead of adding it to the CD, each payment is a little smaller, about $36.75, because interest you withdraw stops earning interest. The monthly payout is P × [(1 + APY)1/12 − 1].
CDs that pay out monthly are useful for retirees who want income; CDs that compound are better if you want the largest balance at maturity.
Calculating CD Interest in Excel or Google Sheets
Both spreadsheets handle the CD formula in a single cell:
| What you want | Formula | Result |
|---|---|---|
| Maturity value from an APY (18 months) | =10000*(1+0.045)^(18/12) | $10,682.54 |
| Maturity value, 7.5% compounded quarterly for 2 years | =FV(0.075/4, 4*2, 0, -10000) | $11,602.22 |
| APY from a 4.75% rate compounded daily | =EFFECT(0.0475, 365) | 4.864% |
| Nominal rate behind a 4.50% APY, monthly | =NOMINAL(0.045, 12) | 4.410% |
| Continuous compounding, $2,000 at 4% for 15 years | =2000*EXP(0.04*15) | $3,644.24 |
FV returns a positive number when the deposit is entered as a negative (money leaving your pocket), which is why the last argument is −10000.
What the Formula Leaves Out: Taxes, Penalties and Inflation
The formula gives your pre-tax interest at maturity. Three things change what you actually keep:
- Income tax. CD interest is taxed as ordinary income in the year it is credited, even if it stays in the CD (your bank reports it on Form 1099-INT). Your after-tax yield is roughly APY × (1 − tax rate): in the 22% federal bracket, a 4.50% APY nets about 3.51%. Inside an IRA CD, the tax is deferred or, in a Roth IRA, avoided.
- Early-withdrawal penalties. Penalties are usually a set number of months of interest. Break a 12-month CD at 4.50% APY after six months, with a three-month penalty, and you keep about $111.87 of the $222.52 earned so far.
- Inflation. The real return is (1 + APY) ÷ (1 + inflation) − 1. Our average CD rates report tracks how the national average compares with inflation every month.
The rate you plug in matters more than any of these. The national average 12-month CD paid 1.76% APY on September 30, 2026, which earns $176 a year on $10,000, while the 1-year Treasury yielded 4.54%. Shopping for a rate near the Treasury yield is worth far more than the difference between daily and monthly compounding.