How interests are calculated on CD investments?

Interest Compounded Daily - Interests of most CDs are compounded daily with a year basis of 365 days.

When the bank offers a CD with a fixed APR, the interest of a CD investment can be calculated as:

$\mathrm{Interest}=\mathrm{Deposit}\times ({(1+{\displaystyle \frac{\mathrm{APR}}{\mathrm{365}}})}^{\mathrm{Days}}-1)$

For example, if a bank offers you a CD with 5.0% APR, you will earn 13.70 interest on the first day with a $100,000.00 deposit.

$\mathrm{Interest}=\mathrm{100000}\times ({(1+{\displaystyle \frac{\mathrm{5.0\%}}{\mathrm{365}}})}^1-1)=13.698630136982=13.70$

You can verify this calculation with our online CD interest calculator by clicking the link: "What Is the 1-day interest of $100,000 deposit for an APR of 5.0% on a 365-day year basis".

When the bank offers a CD with a fixed APY, we need to convert the APY to APR first as shown in the last tutorial:

$\mathrm{APR}=\mathrm{365}\times ({(1+\mathrm{APY})}^{{\displaystyle \frac{1}{\mathrm{365}}}}-1)$

Before using the calculated APR value to calculate daily interest, different banks will round it to different decimal places. For example: a 4.0% APY could be converted to different APR values: 3.92%, 3.9223%, or 3.922282%:

$\mathrm{APR}=\mathrm{365}\times ({(1+\mathrm{4.0\%})}^{{\displaystyle \frac{1}{\mathrm{365}}}}-1)=\mathrm{0.03922282044017}=\mathrm{3.922282\%}=\mathrm{3.9223\%}=\mathrm{3.92\%}$

If you deposit a $100,000.00 to a CD with a 4.0% APY to 2 banks which round the APR value differently: 3.92% and 3.9223%, you will get different interests at the end of the first year: $3,997.63 and $4,000.02. That's about $2.39 difference.

$\mathrm{Interest}=\mathrm{100000}\times ({(1+{\displaystyle \frac{\mathrm{3.92\%}}{\mathrm{365}}})}^{\mathrm{365}}-1)=3997.6269562265=3997.63$
$\mathrm{Interest}=\mathrm{100000}\times ({(1+{\displaystyle \frac{\mathrm{3.9223\%}}{\mathrm{365}}})}^{\mathrm{365}}-1)=4000.0186722148=4000.02$

You can verify this calculation with our online CD interest calculator by clicking the link: "What Is the 365-day interest of $100,000 deposit compounded daily for an APR of 3.9223% on a 365-day year basis".

⇒ Interest Payment on CD Investment

⇐ APR and APY Conversion

⇑ Introduction to CD (Certificate of Deposit)

⇑⇑ CD (Certificate of Deposit)