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What Is a Zero Coupon Bond Formula?

Steven Symes
Steven Symes

A zero coupon bond formula is a mathematical formula that assists investors in calculating how much money they can earn on a zero coupon bond. Calculating the interest earned on a zero coupon bond involves a different formula, since this type of bond does not pay interest with the same structure as other bonds. The zero coupon bond formula is the maturity value of the bond, divided by the result of one plus the investor’s annual yield after it has been divided by two, to the power of the number of years until the maturity of the bond multiplied by two.

How zero coupon bonds operate differs from other bonds, since they pay only a lump sum at the end of the bond’s term. Other bonds pay out coupons, or payments, that are paid by the issuer at scheduled and regular times throughout the term of the bond. A zero coupon bond formula must take this into account, calculating all of the interest earned by the bond, instead of accounting for regular disbursements of the bond’s earnings.

Man climbing a rope
Man climbing a rope

Because of how a zero coupon bond formula is structured, issuers of zero coupon bonds always sell the bonds at a discounted rate. If the issuers were to sell the bonds at the normal face value, as some other bonds might be sold, investors would not spend their money on the bonds. The nature of the formula makes it impossible for investors to gain any money from investing in the bond, unless they do not pay the bond’s face value.

To make up for tying up an investor’s money, a zero coupon bond’s issuer typically will discount the price according to the bond’s maturity date. Bonds that have a maturity date further into the future sell for less than bonds with the same face value, but a maturity date that is not as distant. Investors take a risk when they buy a zero coupon bond with a long term, since the issuer may default on the bond before the term. Unlike other bonds, the investor does not receive periodic payments and so would receive nothing from his investment.

When a person buys a zero coupon bond, or any other type of bond, the issuer of the bond specifies certain terms involved in the transaction. The investor must know what the interest rate for the bond will be, as well as the face value and the maturity date, or the date when the value of the bond will be paid to the investor. Investors must not only use a zero coupon bond formula to calculate how much they stand to earn, but they also must also pay income taxes on the interest the bond earns each year, even though they do not receive any of the money until the bond matures.

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