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There are zero coupon bonds outstanding that have a YTM of 5.37 percent and mature in 19 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?

Question

There are zero coupon bonds outstanding that have a YTM of 5.37 percent and mature in 19 years. The bonds have a par value of $10,000. If we assume semiannual compounding, what is the price of the bonds?

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Solution

To calculate the price of a zero-coupon bond, we use the formula:

P = F / (1 + r/n) ^ nt

where: P = price of the bond F = face value of the bond r = yield to maturity (YTM) n = number of compounding periods per year t = number of years until maturity

Given in the problem: F = $10,000 r = 5.37% or 0.0537 (in decimal form) n = 2 (since it's semiannual compounding) t = 19 years

Substituting these values into the formula, we get:

P = $10,000 / (1 + 0.0537/2) ^ (2*19)

Now, calculate the denominator:

= $10,000 / (1 + 0.02685) ^ 38

= $10,000 / (1.02685) ^ 38

= $10,000 / 2.99234

Finally, calculate the price of the bond:

P = $3343.48

So, the price of the zero-coupon bond is approximately $3343.48.

This problem has been solved

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