Final answer:
To find the current price of a bond that pays a 10 percent coupon on a semiannual basis, with a market rate of 8.8 percent, one must discount the bond's cash flows back to present value using the market rate.
Step-by-step explanation:
To determine the current price of Kevin Rogers' five-year bond that pays a 10 percent coupon on a semiannual basis when the market rate is 8.8 percent, a bond valuation calculation must be performed.
This valuation involves discounting the expected cash flows from the bond (semiannual coupon payments and the face value at maturity) back to the present value using the current market interest rate.
Since the coupon payments are made semiannually, a 10% annual coupon rate means there will be two payments of 5% each per year.
The market rate of 8.8% annually will also be divided by two for each semiannual period, resulting in a 4.4% semiannual rate.
To calculate the present value of these cash flows, each payment and the principal at maturity are discounted by the market rate.
The formula for the present value of an annuity is used to determine the value of coupon payments, while the present value of a single sum formula is utilized for the face value.
Using these calculations and rounding to the nearest dollar, we can find the bond's current price, which typically will be more than the face value since the coupon rate is higher than the market rate.
Therefore, based on given answer options, the correct price would be $1,099.