# How to Calculate Discounted Interest Rates

We are all familiar with interest rates. When you put money in a bank account with interest, you take out more. Compound interest is even more exciting. With compound interest, your interest bears interest. The discount rate is the compound interest rate backwards; instead of calculating the future value of your present money, you calculate the present value of your future money. At equivalent rates, longer periods either increase or discount your money less than shorter periods that combine to the same length. For example, \$100 invested for one year at 10 percent yields \$10 when the interest is given once. When half the interest (5 percent) is given twice (once every six months), the yearly interest then jumps to \$10.25. The more shorter periods, the more the yield. Discounting is the same thing backwards. The more shorter periods, the more the discount.

#### Things You'll Need

• Calculator
• Financial Calculator (optional)

## Instructions

• 1

Add 1 to the periodic interest rate and raise it to the power of periods. The result is the combined rate for all the periods plus 1. Call this the rate plus 1. Subtract 1 for the rate. For example, if your periodic rate is 5 percent every six months, your yearly rate plus 1 is 1.05^2, or 1.1025. The yearly rate is not 10 percent, but .1025, or 10.25 percent.

• 2

Divide 1 by the rate plus 1. This is the discount factor. The discount rate itself is 1 minus the discount factor (or the rate divided by the rate plus 1). For the example above, the discount factor (1/1.1025) is a little more than .907. The discount rate is a little less than .093. The two numbers added together equal 1. (.1025/1.1025 also gives the discount rate.)

• 3

Multiply the future value of your money by the discount factor for the present value. Assume your future value is \$110.25 (\$100 invested plus \$10.25 interest after a year at 5 percent per six months). \$110.25 times the discount factor (a bit more than .907) is \$100. \$110.25 then is worth \$100 now, the opposite of \$100 now worth \$110.25 then. You can also multiply the future value (\$110.25) by the discount rate (a bit less than .093) and subtract the discount (\$10.25) from the future value. These formulas are for discounting one future amount.

• 4

Use the following formula to discount a number of equal cash flows: Divide the (overall) discount rate by the periodic interest rate and multiply by the single cash flow amount. Say the cash flow amount is \$5. Using the numbers above, the discount rate (a bit less than .093) divided by the the periodic rate (.05) equals a little less than 1.86. Multiply this by 5. The present value is a little less than \$9.30. When the interest rate is 5 percent every six months, that is what your two \$5 cash flows (per six months) are worth now.

• 5

Discount the cash flows and future value separately, when both apply. Then add the two present values. This dual calculation is used to determine the present value of coupon bonds. Before, we discounted two \$5 cash flows to a bit under \$9.30. Say you invested \$100, received the two \$5 cash flows (at 5 percent) and remained with \$100. \$100 discounted at 5 percent for two six-month-periods equals a little more than \$90.70. You can see that the two present values combined equal \$100. That is why coupon bonds have the same face and future values; the interest is taken out, while the principal remains the same.

• 6

Use a financial calculator for quick results. Enter the periodic rate, the number of periods, the single cash flow amount (if any) and one future value (if any). The financial calculator computes the present value. Note that the financial calculator returns the amount in the opposite sign of the entered dollar amounts.

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## References

• "Finance"; Ronald W. Melicher; Edgar A. Norton; 2005