# How to Calculate Forward Rates

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Consider a one-year certificate of deposit (CD) paying 4 percent interest and a two-year CD that pays 6 percent. The different rates imply that investors are expecting interest rates to rise in a year's time; otherwise they would be nearly equal. This future rate implied by the difference is called the forward rate. The forward rate in this case is the rate on a one-year CD 12 months from now. When added to the current one-year 4 percent CD, it will make the total return equal to that of the two-year 6 percent CD. Calculating this forward rate can be done with a relatively simple equation using the current rates of return, or spot rates.

### Things You'll Need

• Calculator
• Spot rates

Write out the formula for forward rates: Value of longer investment = (value of shorter investment) x (forward rate + 1)

Compute the value of the investments after interest payments using the same amount of principal. In this example, the final value of \$100 in the 6 percent two-year CD is:

100 x 1.06 x 1.06, which can also be written as 100(1.06)^2 = \$112.36 Note: ^2 means to the second power.

The final value of \$100 in the one-year 4 percent CD is:

100 x 1.04 = \$104

Plug the values into the equation in Step 1 and solve for the forward rate. In this example:

112.36 = 104 x (forward rate + 1)

so

forward rate = (112.36 / 104) - 1 = .0803, or 8.03 percent

Check your work by computing the value of \$100 in a one-year CD at 4 percent rolled into a one-year CD at 8.03 percent. This should equal the value of a two-year CD at 6 percent.

104 x 1.0803 = \$112.35, which is almost the amount computed above for the two-year CD. Had we not rounded the forward rate to 8.03 percent, the values would be equal.

## Tips & Warnings

• When calculating the values of the investments in Step 2, use the correct method of compounding interest (annual, semi-annual, continuous) for the particular investment. The forward rate should use this method as well.

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