Annual percentage yield (APY) is the annualized return on a certificate of deposit, including the effect of compounding. As of ****, you can calculate a CD's APY using the deposit, interest earned, term length and compounding frequency. The formulas below use 365 days in a year.
How to Calculate APY From Total CD Interest
If you know the CD's total interest, use this formula:
[ \text{APY}=\left[\left(1+\frac{\text{Interest}}{\text{Principal}}\right)^{\frac{365}{\text{Days in term}}}-1\right]\times100 ]
- Principal: Initial CD deposit
- Interest: Total interest earned during the CD term
- Days in term: Actual number of days in the CD term
The Consumer Financial Protection Bureau uses this formula for annual percentage yield calculations on time accounts, including CDs.
Example: Calculate APY From CD Interest
Suppose you deposit $1,000 into a six-month CD and earn $30.37 in interest over 182 days.
[ \text{APY}=\left[\left(1+\frac{30.37}{1,000}\right)^{\frac{365}{182}}-1\right]\times100 ]
[ \text{APY}=6.18% ]
The CD's APY is approximately 6.18%.
You do not earn 6.18% during the six-month term. You earn $30.37, which is about 3.04% of the original deposit. APY converts that shorter-term return into an annual figure.
How to Calculate APY From the Interest Rate and Compounding Frequency
If the bank gives you the CD's annual interest rate and compounding frequency, use:
[ \text{APY}=\left(1+\frac{r}{n}\right)^n-1 ]
Multiply the result by 100 to express it as a percentage.
- r: Annual interest rate written as a decimal
- n: Number of compounding periods per year
| Compounding Frequency | n |
|---|---|
| Annually | 1 |
| Semiannually | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
Example: $10,000 CD at 4.80% With Monthly Compounding
[ \text{APY}=\left(1+\frac{0.048}{12}\right)^{12}-1 ]
[ \text{APY}=4.91% ]
The CD's APY is approximately 4.91%.
If the $10,000 deposit remains in the CD for one year, the estimated interest is:
[ $10,000 \times 0.0490702 = $490.70 ]
The maturity value would be approximately $10,490.70, assuming no withdrawals, fees or early-withdrawal penalty.
Interest Rate vs. APY on a CD
The interest rate is the stated rate before compounding. The APY reflects the annual return after accounting for how often the interest compounds. Federal rules define APY as a percentage that reflects the interest paid based on the interest rate and compounding frequency.
| CD Terms | Stated Interest Rate | Approximate APY |
|---|---|---|
| $10,000, one year, no compounding | 4.80% | 4.80% |
| $10,000, one year, monthly compounding | 4.80% | 4.91% |
| $10,000, one year, daily compounding | 4.80% | 4.92% |
With the same stated interest rate, more frequent compounding produces a higher APY.
How to Calculate CD Maturity Value From APY
If you know the deposit, APY and term, estimate the maturity value with:
[ \text{Maturity value}=\text{Principal}\times(1+\text{APY})^{\frac{\text{Days in term}}{365}} ]
Use the APY as a decimal in the formula. For example, 5.00% becomes 0.05.
Example: $5,000 CD at 5.00% APY for 12 Months
For a one-year CD:
[ $5,000\times(1+0.05)^{365/365}=$5,250 ]
The estimated interest is $250, and the maturity value is $5,250.
A six-month CD at the same 5.00% APY would earn less than $250 because the money would remain deposited for only about half a year.
What to Check When Comparing CDs
Use the APY, rather than only the stated interest rate, when comparing CDs with the same term and similar conditions. APY accounts for the effect of compounding.
Also check:
- CD term and maturity date
- Minimum opening deposit
- Whether interest compounds or is paid out
- Early-withdrawal penalty
- Whether the CD renews automatically
- Whether the bank can call the CD before maturity
- Whether the advertised APY applies for the full term
Your actual return may be lower if you withdraw money before maturity and pay an early-withdrawal penalty. The Consumer Financial Protection Bureau recommends comparing the term, interest rate and early-withdrawal penalty when evaluating CDs.
The Easiest Way to Calculate APY on a CD
- Find the initial deposit.
- Find the total interest earned or the stated annual interest rate.
- Convert the CD term into days.
- Identify how often interest compounds.
- Use the total-interest formula or the compounding formula.
- Compare your result with the bank's advertised APY.
For a CD with a specific maturity date, use the original deposit, total interest and actual number of days in the term when those figures are available. Your result may differ slightly from the bank's figure if the bank rounds interest or uses a different disclosed day-count convention.