# 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.

Phiên bản tương tác: https://www.calcopenly.com/vi/finance/cd-calculator
Chủ đề: Máy tính tài chính

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.

## Dữ liệu đầu vào

- **Deposit**
- **Interest rate**
- **Rate is**: Banks advertise the APY, which includes compounding; the APR is the stated rate before compounding (lựa chọn: APY, Tỷ lệ phần trăm hằng năm (APR))
- **Compounding** (lựa chọn: Daily (365), Monthly, Quarterly, Semiannually, Annually, Continuously)
- **Term**
- **Term in** (lựa chọn: Tháng, 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

## Kết quả

- Value at maturity — kết quả chính
- 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)

## Công thức

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

## Ví dụ có lời giải

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

- Deposit: 1000
- Interest rate: 6%
- Rate is: Tỷ lệ phần trăm hằng năm (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%**
- Nguồn đối chiếu: 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: Tỷ lệ phần trăm hằng năm (APR)
- Compounding: Annually
- Term: 36
- Term in: Tháng
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 12 months
- **Value at maturity: 11,576.25**
- **Interest earned: 1,576.25**
- Nguồn đối chiếu: 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: Tháng
- Early withdrawal penalty: 3 months of interest
- Cash out early after: 6 months
- **APR (stated rate): 4.8889%**
- **Value at maturity: 10,500.00**
- Nguồn đối chiếu: 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: Tháng
- 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**
- Nguồn đối chiếu: 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: Tháng
- 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**
- Nguồn đối chiếu: Python decimal: 10,000 × 1.04^(1/12) − 98.057051 = 9,934.680347

### Continuous compounding, taxed interest

- Deposit: 5000
- Interest rate: 3%
- Rate is: Tỷ lệ phần trăm hằng năm (APR)
- Compounding: Continuously
- Term: 24
- Term in: Tháng
- 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**
- Nguồn đối chiếu: Python decimal: 5,000 × e^0.06; APY e^0.03 − 1; penalty 5,000 × 0.03 × 6/12; 309.182733 × 0.76

## Câu hỏi

### 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.

### “CD calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 6. Ví dụ, “Regulation DD example: $1,000 six-month CD, 182 days at 6% compounded daily” được kiểm tra bằng 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 %).

### Phương pháp này lấy từ đâu?

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.

## Nguồn

- [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)

_Chỉ dùng để lập kế hoạch. Bên cho vay, cơ quan thuế và thị trường áp dụng cách làm tròn, phí và quy tắc riêng; hãy xác nhận số liệu với họ trước khi cam kết._