[carabelle]

On December 31, 2005, $210,000 of 11% bonds were issued. The market interest rate at the time of issuance was 12%. The bonds pay interest on June 30 and December 31 and mature in 20 years.

Compute the selling price of a single $1,000 bond on December 31, 2005.

Round all intermediate calculations to three decimal places, and round your final answer to the nearest cent.

[pready]

This is a Present Value Problem, so first start with what you know:
Principle = $210,000, I/R 11%, Market Rate 12% Semiannually, Time = 20yrs
Number of Periods = 40 (20/2), I/R = 5.5% (11/2), Market Rate = 6% (12/2)

Next Compute the value of Interest Payment
$210,000 X 11%/2 = $11,550 Interest

Next Compute the Present Value of the Principle
$210,000 x The Present Value of 1 Table for 40 periods at 6%
$210,000 x .09722 = $20,416.20

Next Compute the Present Value of Interest Payments
$11,550 X Present Value of an ordinary Annuity of 1 Table for 40 periods at 6%
$11,550 X 15.04630 = $173,784.965

Finally add the two Present Values
$20,416.20 + $173,784965 = $194,200.965 which is the Present value of a $210,000 Bond (or the selling price)

[bstewart24]

How did you come up with .09722?

[morgaine300]

Don't know if you're using charts, equations or whatever. But in any case, this all has to be done by compounding periods, which in this case is twice a year. So all interest rates have to be for a half year, cause that's when you stop and compound. And then you need total periods, which is twice the years. You're compounding 2 times a year for 20 years, so 40 total times.

When you're figuring the present value of something, you're using the market rate. You're trying to figure out the value that would yield whatever you'd get in the market. So when going to your charts or equations or calculator or whatever, you're using the 12% (not 11%), divided into compounding periods is 6%.

You're figuring two present values: one on the interest payments, which you didn't actually ask about. And the other on the bond face value. The interest payments are a series of payments and therefore an annuity. But the bond is a lump sum, to be paid back in full at the end of 20 years (or 40 periods). So that's not an annuity. If you're using charts, the chart probably says "present value of $1." There should be no words about annuity or series of payments or at the end of x periods. If you use the 40 periods and 6% interest and find that on the chart, it's the .97222.

If you are using a different method to do this (not charts), you may need to specify how you're doing them, in order to know why you're not getting .97222.