# CD calculator

> Calculate CD interest and maturity value from the APY or APR and compounding, convert APY to APR, and see what an early withdrawal penalty costs.

Interactive version: https://www.calcopenly.com/finance/cd-calculator
Subject: Finance calculators

A certificate of deposit pays a fixed rate for a fixed term. The value at maturity is the deposit times (1 + APR ÷ k) raised to k × years, where k is the number of compounding periods a year; entered as an APY, the same value is the deposit times (1 + APY) raised to the years. The calculator converts between the two rates and shows what breaking the CD early leaves you after a penalty of a set number of months of interest.

With the defaults, $10,000 in a 12-month CD at 4.00% APY compounded daily earns $400.00. That APY equals an APR of 3.9223%. Cashing out after 6 months with a 3-month penalty leaves $10,099.98, since the $98.06 penalty takes about half of the $198.04 earned by then.

The penalty is computed as simple interest on the deposit at the APR. Deposit agreements differ, and Regulation DD requires the bank to disclose how its penalty is calculated. Terms in months use 365 ÷ 12 days per month.

## Inputs

- **Deposit**
- **Interest rate**
- **Rate is**: Banks advertise the APY, which includes compounding; the APR is the stated rate before compounding (options: APY, APR)
- **Compounding** (options: Daily (365), Monthly, Quarterly, Semiannually, Annually, Continuously)
- **Term**
- **Term in** (options: Months, Days)
- **Early withdrawal penalty**: From your deposit agreement; 90 days is about 3 months
- **Cash out early after**
- **Tax rate on interest**: Your marginal rate; CD interest is taxed as ordinary income

## Results

- Value at maturity — main result
- Interest earned
- APY
- APR (stated rate)
- Interest after tax
- Early withdrawal penalty
- Cash-out value after the penalty
- Gain if cashed out early
- Penalty covered after (months)

## Formula

$$
A = P\left(1+\tfrac{r}{k}\right)^{kt} = P(1+\text{APY})^{t},\qquad \text{APY} = \left(1+\tfrac{r}{k}\right)^{k}-1,\qquad \text{penalty} = P\,r\,\tfrac{m}{12}
$$

## Worked examples

### Regulation DD example: $1,000 six-month CD, 182 days at 6% compounded daily

- Deposit: 1000
- Interest rate: 6%
- Rate is: APR
- Compounding: Daily (365)
- Term: 182
- Term in: Days
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 3 months
- **Interest earned: 30.37**
- **APY: 6.1831%**
- Checked against: 12 CFR 1030 Appendix A, Part I.A, example (2): interest $30.37, APY 6.18% (Python decimal: (1 + 0.06/365)^365 − 1 = 6.183131 %)

### $10,000 at 5% compounded yearly for 3 years

- Deposit: 10,000
- Interest rate: 5%
- Rate is: APR
- Compounding: Annually
- Term: 36
- Term in: Months
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 12 months
- **Value at maturity: 11,576.25**
- **Interest earned: 1,576.25**
- Checked against: calculator.net CD calculator default inputs (10,000, 5%, 3 years, annually) and its published result, $11,576.25 and $1,576.25 interest

### APY 5% compounded monthly converts to APR

- Deposit: 10,000
- Interest rate: 5%
- Rate is: APY
- Compounding: Monthly
- Term: 12
- Term in: Months
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 6 months
- **APR (stated rate): 4.8889%**
- **Value at maturity: 10,500.00**
- Checked against: Python decimal: 12 × (1.05^(1/12) − 1) = 4.888949 %; one year at 5% APY is 10,500 by definition

### Defaults: $10,000, 4% APY daily, 12 months, 3-month penalty after 6 months

- Deposit: 10,000
- Interest rate: 4%
- Rate is: APY
- Compounding: Daily (365)
- Term: 12
- Term in: Months
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 6 months
- **Interest earned: 400.00**
- **APR (stated rate): 3.9223%**
- **Early withdrawal penalty: 98.06**
- **Cash-out value after the penalty: 10,099.98**
- **Penalty covered after: 3.0 months**
- Checked against: Python decimal: r = 365 × (1.04^(1/365) − 1); penalty 10,000 × r × 3/12; 10,000 × 1.04^0.5 − penalty

### Penalty larger than the interest earned (cash out after 1 month)

- Deposit: 10,000
- Interest rate: 4%
- Rate is: APY
- Compounding: Daily (365)
- Term: 12
- Term in: Months
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 1 month
- **Cash-out value after the penalty: 9,934.68**
- **Gain if cashed out early: -65.32**
- Checked against: Python decimal: 10,000 × 1.04^(1/12) − 98.057051 = 9,934.680347

### Continuous compounding, taxed interest

- Deposit: 5000
- Interest rate: 3%
- Rate is: APR
- Compounding: Continuously
- Term: 24
- Term in: Months
- Early withdrawal penalty: 6 months of interest
- Cash out early after: 12 months
- Tax rate on interest: 24%
- **Value at maturity: 5,309.18**
- **APY: 3.0455%**
- **Early withdrawal penalty: 75.00**
- **Cash-out value after the penalty: 5,077.27**
- **Interest after tax: 234.98**
- Checked against: Python decimal: 5,000 × e^0.06; APY e^0.03 − 1; penalty 5,000 × 0.03 × 6/12; 309.182733 × 0.76

## Questions

### How is interest on a CD calculated?

Multiply the deposit by (1 + APR ÷ k) to the power k × years, where k is the compounding periods per year, and subtract the deposit. $10,000 at a 5% APR compounded yearly for 3 years grows to 10,000 × 1.05³ = $11,576.25, so the interest is $1,576.25. With the rate given as an APY, use (1 + APY) to the power of the years instead.

### What is the difference between APY and APR on a CD?

The APR is the stated yearly rate before compounding; the APY includes compounding and shows what $100 earns in a year. A 5% APY compounded monthly is an APR of 4.8889%, and a 6% APR compounded daily is an APY of 6.1831%. Regulation DD (Truth in Savings) requires banks to disclose both, and the APY is the one to compare CDs on.

### What is the penalty for withdrawing a CD early?

Whatever the deposit agreement says, usually a number of months or days of interest. The federal minimum is in Regulation D: money withdrawn within six days of deposit must lose at least seven days' simple interest. On $10,000 at a 3.9223% APR, a 3-month penalty is 10,000 × 0.039223 × 3 ÷ 12 = $98.06.

### Can an early withdrawal penalty eat into the principal?

Yes, when the penalty is larger than the interest earned so far. On $10,000 at 4% APY, one month earns $32.74, but a 3-month penalty is $98.06, so cashing out returns $9,934.68 and you lose $65.32 of your deposit. With these terms the penalty is covered after about 3 months.

### Are CDs FDIC insured?

Yes. The FDIC lists certificates of deposit among insured deposits, covered up to $250,000 per depositor, per insured bank, for each account ownership category. Coverage is principal plus interest accrued through the date the bank fails, so a $245,000 deposit at 4% APY passes the limit after about 6.2 months.

### How accurate is the CD calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “Regulation DD example: $1,000 six-month CD, 182 days at 6% compounded daily” is checked against 12 CFR 1030 Appendix A, Part I.A, example (2): interest $30.37, APY 6.18% (Python decimal: (1 + 0.06/365)^365 − 1 = 6.183131 %).

### Where does the method come from?

12 CFR 1030 (Regulation DD, Truth in Savings), Appendix A: annual percentage yield calculation; 12 CFR 204.2(c)(1)(i) (Regulation D): minimum early withdrawal penalty on time deposits; 12 CFR 1030.4(b)(6)(ii): disclosure of early withdrawal penalties; FDIC: Understanding deposit insurance.

## Sources

- [12 CFR 1030 (Regulation DD, Truth in Savings), Appendix A: annual percentage yield calculation](https://www.ecfr.gov/current/title-12/part-1030/appendix-Appendix%20A%20to%20Part%201030)
- [12 CFR 204.2(c)(1)(i) (Regulation D): minimum early withdrawal penalty on time deposits](https://www.ecfr.gov/current/title-12/section-204.2)
- [12 CFR 1030.4(b)(6)(ii): disclosure of early withdrawal penalties](https://www.ecfr.gov/current/title-12/section-1030.4)
- [FDIC: Understanding deposit insurance](https://www.fdic.gov/resources/deposit-insurance/understanding-deposit-insurance)

_Note: financial information, not professional advice._