The CD formula
Balance at maturity = Deposit × (1 + APY)months / 12. Interest earned is the balance minus the deposit. If you only know the interest rate r and the compounding frequency n, first convert it: APY = (1 + r / n)n − 1.
Example with steps: $15,000 CD at 3% compounded daily for 5 years
A common homework question: a CD opens with a $15,000 deposit at a 3% interest rate compounded daily. What is the balance and the interest after five years?
- Formula: A = P × (1 + r / n)n × t, with P = $15,000, r = 0.03, n = 365 compounding periods a year and t = 5 years.
- Rate per day: r / n = 0.03 / 365 = 0.00008219.
- Number of periods: n × t = 365 × 5 = 1,825.
- Growth factor: (1 + 0.00008219)1,825 = 1.16183.
- Balance: A = $15,000 × 1.16183 = $17,427.41.
- Interest earned: $17,427.41 − $15,000 = $2,427.41.
Interest rate versus APY: a 3% rate compounded daily is an APY of (1 + 0.03 / 365)365 − 1 = 3.045%. The APY is slightly higher because interest earns interest during the year. With the APY the same balance is $15,000 × (1 + 3.045%)5 = $17,427.41. To try it in the calculator above, choose the interest rate (APR) type, set daily compounding, 3%, $15,000 and 60 months.
Example: $10,000 CD at 4.5% APY
| Term | Balance at maturity | Interest earned |
|---|---|---|
| 3 months | $10,110.65 | $110.65 |
| 6 months | $10,222.52 | $222.52 |
| 12 months | $10,450.00 | $450.00 |
| 18 months | $10,682.54 | $682.54 |
| 24 months | $10,920.25 | $920.25 |
| 36 months | $11,411.66 | $1,411.66 |
| 60 months | $12,461.82 | $2,461.82 |
A 4.5% APY corresponds to an interest rate of about 4.402% compounded daily, or 4.41% compounded monthly.
Interest on a $10,000 CD by APY and term
| APY | 6 months | 1 year | 2 years | 5 years |
|---|---|---|---|---|
| 3% | $148.89 | $300.00 | $609.00 | $1,592.74 |
| 4% | $198.04 | $400.00 | $816.00 | $2,166.53 |
| 4.5% | $222.52 | $450.00 | $920.25 | $2,461.82 |
| 5% | $246.95 | $500.00 | $1,025.00 | $2,762.82 |
How to compare CDs
Compare by APY rather than by rate, check the term matches when you will need the money, and look at the early-withdrawal penalty. If you might need part of the money sooner, a CD ladder (splitting the deposit across 1-, 2- and 3-year CDs) or a high-yield savings account keeps more of it within reach.