The Florida Investment Fund buys 94 bonds of the Gator Corportation through a br

Question

The Florida Investment Fund buys 94 bonds of the Gator Corportation through a broker. The bonds pay 10 percent annual interest. The yield to maturity (market rate of interest) is 12 percent. The bonds have a 20 year maturity.Using an ssumption of semiannual interest payments.

a) Compute the price of a bond. ( Round the PV Factor to 3 decimal places and final answer to 2 decimal places.)

b) Compute the total value of the 94 bonds. (Round the PV Factor to 3 decimal places and final answer to 2 decimal places.)

Explanation / Answer

At 6%, PV = 1,573.50; at 8%, PV = 1,294.54; at 12%, PV = 925.31

Determine Annuity amount by using Face amount of Bond and Face rate of Interest. Here it is $110. But when using PV of $1 and PV Annuity tables, always use market rates, or YTM.

Let%u2019s use the following formula to compute the present value of the interest payments only as of January 1, 2012 for the bond described above. The amount of the interest payment occurring at the end of each six-month period is represented by %u201CPMT%u201D, the number of semiannual periods is represented by %u201Cn%u201D and the market interest rate per semiannual period is represented by %u201Ci%u201D.

The present value of $36,500 tells us that an investor requiring an 8% per year return compounded semiannually would be willing to invest $36,500 on January 1, 2012 in return for 10 semiannual payments of $4,500 each%u2014with the first payment occurring on June 30, 2012. The difference between the 10 future payments of $4,500 each and the present value of $36,500 equals $8,500 ($45,000 minus $36,500). This $8,500 return on an investment of $36,500 gives the investor an 8% annual return compounded semiannually.

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