Every bond has a stated face value, interest rate and maturity date. The face value serves two purposes: to determine how much the bond issuer has to pay back when the bond matures in the future and, along with the interest rate, to determine how much interest must be paid over the life of the bond. However, bonds aren’t always sold for face value, especially if investors expect to earn a higher return than the stated interest rate. As a result, bonds can be sold at a discount. To determine whether a discounted bond is worth your investment, you need to know how to calculate the effective interest rate.

## Purpose of Bond Discounts

Each bond has a face value, which is the amount of principal the bond issuer will pay back to the bondholder when the bond matures. However, depending on the interest rate offered by the bond, bond buyers may not be willing to pay the full face value to acquire the bond. For example, say a corporate bond pays 5 percent. However, based on the market rates for similar bonds, buyers expect a 7-percent return on their investment to make it worthwhile to buy the bonds. Instead of demanding that the company issue bonds with a higher interest rate, bond buyers will offer less than the face value to purchase the bond. That way, between the interest payments and the full face value they receive when the bond matures, the investors achieve the effective interest rate they desire on their investment.

## Effective Interest Rate Formula

First, calculate the amount of the discount by subtracting the bond’s price from its face value. Second, divide the result by the number of bond payments remaining before the bond matures. Third, add the interest received per bond payment by the result. Fourth, divide the result by the average of the discounted price paid for the bond and the bond’s face value. Finally, multiply the result by 100 to find the effective interest rate for the discounted bond.

For example, say there is a 10-year bond with a face value of $2,000 that pays 5 percent interest every year and returns the principal when the bond matures. At 5 percent interest, the bond will pay $100 per year in interest. If the bond is being sold at a discount for $1,900, first subtract the sale price of $1,900 from $2,000 to find the bond is being sold at a $100 discount. Second, divide the $100 discount by the 10 annual payments remaining on the bond to get $10. Third, add the $10 to the $100 in interest the bond pays each year to get $110. Fourth, divide $110 by the average of $1,900 and $2,000, or $1,950, to get 0.0564. Finally, multiply 0.0564 by 100 to find the effective interest rate is 5.64 percent.

#### References

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- How to Calculate Nominal Yield
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- How to Find the Interest Rate on a Bond
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- How to Calculate Weighted Duration Bond
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