Final answer:
To calculate the bond's current price with a 7 percent coupon, a yield to maturity of 5.00 percent and 18 years to maturity, we must discount the annual coupon payments and the face value to present value. The bond's current price would be $1,241.20.
Step-by-step explanation:
The current price of a bond can be calculated by discounting the future cash flows (coupon payments and face value) back to the present using the yield to maturity. Since the bond pays annual interest, we can use the formula for present value of an annuity and the present value of a lump sum to find the price.
First, calculate the present value of the coupon payments, which are an annuity. The annual coupon payment is 7% of the $1,000 face value, which is $70 per year for 18 years. Using the formula, we have:
Present Value of Coupons = C * [(1 - (1 + r)^-n) / r]
where C = annual coupon payment, r = yield to maturity, and n = number of years
This gives us:
Present Value of Coupons = $70 * [(1 - (1 + 0.05)^-18) / 0.05]
Next, calculate the present value of the $1,000 face value, which will be received in 18 years:
Present Value of Face Value = FV / (1 + r)^n
This gives us:
Present Value of Face Value = $1,000 / (1 + 0.05)^18
Adding both present values gives us the total current price of the bond.
Direct answer in 2 lines: The bond's current price, if the yield to maturity is 5.00 percent is $1,241.20.