[keagangriffin]

Matthew Company issued 10-year, 7% bonds (paying semiannual interest) with a par value of $100,000. The market
rate of interest when the bonds were issued was 6%. Compute the price of the bonds when they were issued.
A) $107,360.70
B) $93,206.05
C) $107,441.25
D) $93,290.70
E) $107,018.80


ANSWER: C

I cannot figure out why!

[ArcSine]

First, schedule out the cash flows to an investor from these bonds--the semiannual coupon payments, plus the redemption amount (face amount) paid at maturity. Then you'll need to discount ("present value") that cash flow stream by the market interest rate. Remember to adjust the discount rate for semiannual periods--i.e. you'll be using 3% per period, and there'll be 20 periods.

If you're familiar with the basic present value formulas, you can shortcut it by noting that the 20 coupon payments form an annuity, and then the redemption payoff amount can be discounted as a single amount. Or equivalently, treat it as a 19-period annuity, followed by a single amount of 103,500 at the 20th period.