# How to Calculate the Future Value of a CD

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A CD (certificate of deposit) is a fixed-rate time deposit offered by banks and credit unions. CDs are extremely safe, since they are insured by the federal government. CDs are popular with investors because they pay higher interest rates than regular savings accounts. In exchange for the higher interest, the investor agrees to leave the money on deposit for a specified period of time called the "maturity" and to be assessed a penalty for withdrawing the money early. The future value of a CD is affected by both the interest rate and the terms of the deposit agreement.

Look at the information that you received when you bought the CD. If the interest earned is paid out to you periodically instead of being added to the balance of the CD, the value of the CD won’t change. The future value of a CD of this type is the same as when it was bought. However, if the interest is added to the CD balance periodically, the value of the CD will increase on a regular basis. The future value is determined by how often the interest is compounded (calculated and added to the principal balance). Steps 2 to 4 explain how compounding works in principle. Step 5 explains the formula that you would use in practice to find the future value of a CD.

Find the periodic interest rate. This is the proportion of interest that accumulates between compounding dates. To find the periodic interest rate, divide the annual interest rate by 365 (the number of days in the year) and multiply by the number of days between each compounding calculation. For example, if the interest rate is 4.38 percent and the interest is compounded weekly, the periodic rate is 0.0438 (4.38 percent) divided by 365 and then multiplied by 7, giving 0.00084 (0.084 percent).

Start to calculate the future value of a CD at a given point in time by taking the initial value of the CD as your starting balance. Multiply by the periodic interest rate (from Step 2) and add the result to the CD. For instance (continuing the example from Step 2), if the CD is for \$10,000, multiply by 0.00084 (0.084 percent) to find the first week’s interest (\$8.40). Add to the balance to get \$10,008.40 as the first week’s ending balance.

Use the ending balance as the starting balance of the next week and repeat Step 3 until you have calculated the future value of the CD for the period of time you want. If you want to know the future value after one year, you would repeat 52 times in our example. If you have a long-term CD (say five years), you would repeat the calculation 5 times 52, or 260 times.

Use a formula to simplify calculation of the future vale of a CD. The method above illustrates the principle of compounding, but it’s much easier to program a calculator with the formula that concisely expresses the method in steps 1 through 4. The formula is F = P x I^R, where F is the future value, P is the principal and I^R is (1 plus the periodic rate raised to R, which is the number of compounding periods). The same example used above for one year (52 compounding periods of 7 days) is \$10,000 x 1.00084^52. The future value of the CD after one year works out to \$10,447.54

#### Tips

• In practice, it’s much easier to calculate the future value of a CD by using an online compound interest calculator. There is a link to one under Resources.