# How to Calculate Compounding & Discounting

by Bryan Keythman

An investment’s present value is its value today, while its future value is its value at a point sometime in the future. Compounding occurs when an investment earns interest on its initial investment amount and on its accumulated interest. You can use the future value formula to calculate the effects of compounding to determine an investment’s future value. Discounting is the reverse effect of compounding. You use discounting to determine how much you need to invest today to achieve a specific future value. You can use the present value formula to discount an investment.

1. Determine an investment’s present value, which is the initial amount you invest today. Also determine the interest rate at which it will compound annually and the number of years into the future it will compound. For example, assume you want to know how much a savings account will be worth in five years if you deposit \$1,000 today and it compounds at 3 percent annually.

2. Substitute the values into the future value formula: PV(1 + R)^N. In the formula, PV represents the present value, R represents the decimal form of the annual interest rate and N represents the number of years the investment will compound. In this example, substitute the values to get \$1,000(1 + 0.03)^5.

3. Add the numbers inside parentheses. Raise the result to the power of the exponent. Then multiply that result by the present value to compound it to the future value. In this example, add 1 to 0.03 to get 1.03. Raise 1.03 to the fifth power to get 1.159. Multiply 1.159 by \$1,000 to get a future value of \$1,159. This means that \$1,000 compounded at 3 percent annually will grow to \$1,159 in five years.

4. Determine an investment’s future value, the number of years into the future the investment will attain that value and the investment’s annual interest rate. Using the numbers from the previous example, assume you want to know how much you need to invest today to get a future value of \$1,159 in five years if the investment earns 3 percent interest annually.

5. Substitute the values into the present value formula: FV/[(1 + R)^N]. In the formula, FV represents the future value, N represents the number of years needed to attain that value and R represents the decimal form of the annual interest rate. In this example, substitute the values to get \$1,159/[(1 + 0.03)^5].

6. Add the numbers in parentheses. Raise your result to the power of the exponent. Divide the future value by that result to discount the future value to the present value. Continuing with the example, add 1 to 0.03 to get 1.03. Raise 1.03 to the fifth power to get 1.159. Divide \$1,159 by 1.159 to get a \$1,000 present value. This means you must invest \$1,000 today at 3 percent annual interest to grow the investment to \$1,159 in five years.