CD Calculator

What this calculator answers

How much a certificate of deposit (CD) will be worth when it matures, and how much of that is interest, from the APY a bank advertises or from the interest rate and compounding in the account disclosure. Check Estimate an early withdrawal and it also answers the question most CD holders ask later: what closing the CD before maturity would pay after the penalty, whether the penalty eats into your deposit, and how high a new CD’s APY must be for breaking this one to pay off.

How to use it

• Deposit: the amount you put in at the start, in dollars. 15,000, $15,000 and 15k all work.
• Term: the CD’s length in months, up to 120. A 5-year CD is 60 months; if you type a small number such as 5, the calculator reminds you that it reads it as months.
• Rate you’re entering: choose APY for the annual percentage yield banks advertise, or Interest rate for the rate before compounding. The disclosure lists both. Under the rate box, the calculator shows the other figure.
• Compounding: how often interest is added, from the disclosure. With an APY it doesn’t change the value at maturity, but it sets the equivalent interest rate that penalties use.
• Early withdrawal (optional): the Penalty and its unit (months or days of interest), what it is charged on (the deposit, or the deposit plus the interest earned), the month you’d Withdraw after, and, to compare breaking the CD, the New CD’s APY you’ve been offered.

Results update as you type. The month-by-month table downloads as a CSV file, and a second table shows the same deposit and rate over terms from 3 to 60 months. The Try buttons switch to a 6-month term or a 5-year CD at 4%, or close the example CD early at month 6 or month 2. To compare two offers, press Save for comparison, change the inputs and save again. Continue in the APY Calculator takes the rate and deposit across to see the rate at every compounding frequency, and Continue in the Compound Interest Calculator takes the deposit, rate and term across so you can add regular deposits, which this calculator doesn’t model.

How much interest will my CD earn?

Grow the deposit by the APY for the number of years in the term, then subtract the deposit. An APY is a year’s interest as a share of the deposit with compounding already counted, so the term in months divided by 12 is all the formula needs:

$$A = P \times (1 + \text{APY})^{\,\text{months}/12} \qquad I = A - P$$

• $A$ is the value at maturity, and $I$ the interest earned.
• $P$ is the deposit.
• $\text{APY}$ is the annual percentage yield as a decimal (4.10% is 0.041).

With an interest rate $r$ compounded $m$ times a year instead, $A = P \times (1 + r/m)^{\,m \times \text{months}/12}$.

Worked example: $15,000 at 4.10% APY for 18 months

1. Time in years: t = 18 ÷ 12 = 1.5.
2. Value at maturity: A = $15,000 × $1.041^{1.5}$ = $15,931.89.
3. Interest: I = $15,931.89 − $15,000 = $931.89.

After 12 months the balance is exactly $15,615.00: $615.00 is 4.10% of $15,000, which is what the APY promises for a year. Each month earns a little more than the last, from $50.31 in month 1 to $53.26 in month 18, because the interest already added earns interest too.

The same deposit at the same APY over other terms:

A bank may pay a different rate for each term, so compare terms with the rate quoted for each one.

APY or interest rate: which number should you enter?

Enter the APY when you have it: it already includes compounding, and Regulation DD requires the account disclosure to state it. An interest rate means something only together with its compounding frequency, which the disclosure also gives. The two convert like this:

$$\begin{gathered} \text{APY} = \left(1 + \frac{r}{m}\right)^{m} - 1 \\ r = m\left[(1 + \text{APY})^{1/m} - 1\right] \end{gathered}$$

A 4.10% APY is these interest rates:

Is CD interest compounded daily or monthly? It depends on the CD; the disclosure states how often interest is compounded and credited. For the value at maturity it doesn’t matter once you have the APY. It matters when you convert the APY to an interest rate, and penalties are figured on the interest rate.

Worked example with an interest rate: a 5-year CD at 4% compounded monthly. The monthly rate is 0.04 ÷ 12 = 0.00333333 and there are 12 × 60 ÷ 12 = 60 compounding periods, so A = $15,000 × $(1 + 0.04 \div 12)^{60}$ = $18,314.95. Its APY is $(1 + 0.04 \div 12)^{12} - 1$ = 4.0742%, which is why the 4.10% APY above reaches $18,337.70 over the same 60 months, $22.75 more.

How CD early withdrawal penalties are calculated

The penalty is a number of days’ or months’ interest, figured as simple interest at the CD’s interest rate (not the APY). Your account disclosure must say how your penalty is calculated, so check it against this:

$$\text{penalty} = \text{base} \times r \times \frac{N}{12}$$

• $N$ is the number of months of interest. For a penalty stated in days, use $N \div 365$ in place of $N \div 12$.
• $r$ is the interest rate as a decimal.
• The base is the deposit or, if your disclosure charges the penalty on the amount withdrawn, the whole balance with its interest when you close the CD.

You receive the balance minus the penalty.

Worked example: closing the $15,000 CD after 6 months

Take a penalty of 6 months of interest on the deposit.

1. Balance after 6 months: $15,000 × $1.041^{0.5}$ = $15,304.41, so $304.41 of interest has been earned.
2. Interest rate: a 4.10% APY compounded daily is 4.0184%, or 0.040184.
3. Penalty: $15,000 × 0.040184 × 6 ÷ 12 = $301.38.
4. Amount received: $15,304.41 − $301.38 = $15,003.03.

Keeping the CD to maturity would pay $15,931.89, which is $928.86 more. Two other ways a disclosure might state the same penalty:

• 180 days of interest: $15,000 × 0.040184 × 180 ÷ 365 = $297.25, so you’d receive $15,007.16.
• 6 months of interest on the amount withdrawn (deposit plus interest): $15,304.41 × 0.040184 × 6 ÷ 12 = $307.50, so you’d receive $14,996.91, which is $3.09 less than you deposited.

Can an early withdrawal penalty cut into your principal?

Yes. When the penalty is larger than the interest earned so far, the difference comes out of your deposit. Close the same CD after 2 months and it has earned $100.79, but the penalty is still $301.38, so you’d get back $14,799.41, which is $200.59 less than you put in. Right after opening you’d get back $14,698.62. From month 6 on, the interest earned covers this penalty.

For money withdrawn within six days of the deposit, Federal Reserve Regulation D sets a minimum penalty of seven days’ simple interest. Otherwise the amount is set by your account agreement, as the disclosure describes it. The month-by-month table shows what closing the CD at the end of each month would pay and marks every month that returns less than the deposit.

Is it worth breaking a CD for a higher rate?

Only if the new CD’s APY is above the break-even rate: the APY at which the amount you’d receive grows back to what keeping the old CD would pay, by the same date.

$$\text{break-even APY} = \left(\frac{A}{R}\right)^{12/n} - 1$$

• $A$ is the value at maturity if you keep the CD.
• $R$ is the amount you’d receive after the penalty.
• $n$ is the number of months left in the term.

Closing the example CD after 6 months leaves 12 months, so the break-even APY is $(15{,}931.89 \div 15{,}003.03)^{12/12} - 1$ = 6.19%. A new 12-month CD at 5.25% APY would grow the $15,003.03 to $15,003.03 × 1.0525 = $15,790.69 by the original maturity date, so keeping the old CD comes out $141.20 ahead. Closing after 2 months, the new CD has 16 months to catch up, and the break-even APY is 5.69%.

The break-even rate is well above the old 4.10%, because the new CD first has to earn back the penalty. When you shop, compare offers for the exact number of months left, and read the new CD’s own penalty terms.

Reading the result

• The headline is the value at maturity. With an early withdrawal before maturity, it is what you’d receive instead.
• The tiles give the interest earned, the equivalent interest rate (or the APY, if you entered an interest rate) and the average interest a month. With an early withdrawal, they show the interest earned by then, the penalty and what keeping the CD would pay.
• Break it and reinvest? states the break-even APY. With a new CD’s APY entered, it compares both choices in dollars at the original maturity date and says which comes out ahead.
• The month-by-month table lists each month’s interest and the balance. With an early withdrawal it adds the penalty and what you’d receive for closing the CD in that month, marked “(below deposit)” where the penalty eats into your deposit.
• The chart draws the balance over the term and, with an early withdrawal, the amount you’d receive each month next to your deposit.
• Interest over other terms repeats the calculation for 3 to 60 months at your deposit and rate.
• A withdrawal month at or after the end of the term has no penalty; the calculator says so and shows the value at maturity.

What happens when a CD matures?

You can take the money out without an early withdrawal penalty. What happens if you do nothing depends on the renewal terms in your disclosure, which must say whether the CD renews automatically and how long any grace period lasts. For a CD longer than one month that renews automatically, the bank must send a notice at least 30 days before maturity, or at least 20 days before the end of a grace period of five days or more. The renewed CD can carry a different rate. This calculator stops at maturity; to see a renewed term, run it again with the new rate and the maturity value as the deposit.

Assumptions and limitations

• The rate is fixed for the whole term. Variable-rate and step-up CDs aren’t modeled.
• One deposit at the start, and all interest stays in the CD until maturity. A CD that pays its interest out earns less than shown.
• A month counts as one twelfth of a year. Banks count actual days (a 6-month term runs 181 to 184 days, where this calculator counts 182.5), so a statement can differ by a day or two of interest, plus a few cents from rounding each interest credit.
• With an interest rate that compounds quarterly, twice a year or once a year, a term that ends between compounding dates gets a fractional last period in $(1 + r/m)^{n}$. A bank that pays simple interest for that part period pays slightly more.
• The penalty is simple interest for a number of months or days at the interest rate, charged on the deposit or on the whole balance, and it is never more than the balance. If your disclosure describes it another way, check the bank’s own figure. Closing early means withdrawing the whole CD; partial withdrawals aren’t modeled.
• Breaking and reinvesting assumes a new CD for exactly the months left, at a fixed APY, with no further penalty or fees.
• Taxes and inflation are not included. Inflation can outpace a CD’s interest, so the dollars at maturity may buy less than today.
• The result is an educational estimate, not financial advice or a bank’s quote.

Common mistakes

• Entering the APY as the interest rate. Typing 4.10 as a daily-compounded interest rate turns it into a 4.185% APY and overstates the example by $19.51. Enter the APY as the APY.
• Figuring the penalty on the APY. Penalties use the interest rate: 6 months of interest at the 4.10% APY would be $307.50, which is $6.12 more than the $301.38 at the 4.0184% interest rate.
• Assuming a penalty only takes interest. Early in the term the interest earned can be smaller than the penalty, so you get back less than you deposited.
• Comparing a new rate with the old APY. A new CD has to beat the break-even APY, not the old one, because it must first make up the penalty.
• Typing the term in years. The term is in months: a 3-year CD is 36, not 3.