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Assume that the City of New York sold an issue of $1,000 maturity value, tax exe

ID: 2766074 • Letter: A

Question

Assume that the City of New York sold an issue of $1,000 maturity value, tax exempt (muni), zero coupon bonds 5 years ago. The bonds had a 10-year maturity when they were issued, and the interest rate built into the issue was nominal 7.20 percent, but with semiannual compounding. The bonds are not callable at a premium of 10 percent over the accrued value. What nominal and effective annual rate of return would an investor, who bought the bonds when they were issued and who still owns them, earn if they are called today?

Explanation / Answer

Price of Zero coupon bond = Maturity value / (1+i)n

Price of Zero coupon bond = $1,000 / (1 + 0.072)10

Price of Zero coupon bond = $1,000 * 0.4989

Price of Zero coupon bond = $499

Price of Zero coupon bond after 5 years = $1,000 / (1 + 0.072)5

Price of Zero coupon bond after 5 years = $1,000 * 0.7063

Price of Zero coupon bond after 5 years = $706

Nominal return:

                $499 = $706 / (1+i)5

                (1+i)5 = $706 / $499 = 1.41

                I = Nominal Return = 9.63%