What Is APR Calculation Formula for Bank CDs?

If you know the compounding frequency of a bank CD (Certificate of Deposit) and its APY (Annual Percentage Yield), you can calculate the interest rate, also called APR (Annual Percentage Rate), of the CD using the following formula:

$\mathrm{APR}=N\times ({(1+\mathrm{APY})}^{\frac{1}{N}}-1)$
$N=\text{Number of compounding periods in a year}$

For example, the APR of a 1-year CD with a 5.116% APY compounding monthly will be:

$\mathrm{APR}=12\times ({(1+0.05116)}^{\frac{1}{12}}-1)=0.049998186967054714=\mathrm{5.00\%}$

So if you invest $1,000.00 in this CD, you will earn an interest of 5.116% * $1,000.00 = $51.16 in a year. Your deposit balance will be $1,051.16 when the CD matures.

We can validate this by calculating monthly interests and compounding them to your deposit balance for 12 months:

End of month 1: 1000.00*(1.0+0.05/12) = 1004.17
End of month 2: 1004.17*(1.0+0.05/12) = 1008.35
End of month 3: 1008.35*(1.0+0.05/12) = 1012.55
End of month 4: 1012.55*(1.0+0.05/12) = 1016.77
End of month 5: 1016.77*(1.0+0.05/12) = 1021.01
End of month 6: 1021.01*(1.0+0.05/12) = 1025.26
End of month 7: 1025.26*(1.0+0.05/12) = 1029.53
End of month 8: 1029.53*(1.0+0.05/12) = 1033.82
End of month 9: 1033.82*(1.0+0.05/12) = 1038.13
End of month 10: 1038.13*(1.0+0.05/12) = 1042.46
End of month 11: 1042.46*(1.0+0.05/12) = 1046.80
End of month 12: 1046.80*(1.0+0.05/12) = 1051.16

For other APR calculation examples, visit our APR Calculator for Term Deposits.

⇒ APR/APY Examples of Bank CDs

⇐ APY Calculation Formula for Bank CDs

⇑ Introduction on CD (Certificate of Deposit)

⇑⇑ Fixed Income Investments