A bond has 7 years to maturity, an 8% coupon, a $1,000 face value, and pays interest semiannually. What is the bond's current price if the yield to maturity is 7.32%?

Question

Quizplus · Accepted Answer

The bond's current price can be calculated using the formula for the present value of a bond, which includes the present value of the annuity (coupon payments) and the present value of the face value (lump sum at maturity). Given the semiannual interest payments, the effective yield per period is 7.32%/2 = 3.66%, and there are 7*2 = 14 periods. The present value of the annuity (coupon payments) is calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the semiannual coupon payment ($1,000 * 8% / 2 = $40), r is the semiannual yield (3.66%), and n is the total number of payments (14). The present value of the face value is calculated using the formula PV = FV / (1 + r)^n, where FV is the face value ($1,000). Adding these two components gives the bond's current price, which matches the value provided in option E, $1,036.73.

A Bond Has 7 Years to Maturity, an 8% Coupon