The Price Perpetual Bank has purchased a bond that has a coupon rate of 5.5% and a face value of $1000.It has 11 years to maturity and is currently selling in the market for $887.52.The bond makes annual coupon payments.What is the yield-to-maturity on this bond?
A)7%
B)5.5%
C)11%
D)4.70%
E)None of the options is correct

Question

Quizplus · Accepted Answer

The yield-to-maturity (YTM) can be calculated using the formula for the present value of a bond, which equates the current market price of the bond to the sum of the present value of its future coupon payments and the present value of its face value. The YTM is the rate (r) that solves the equation: $887.52 = ($55 / (1 + r)^1) + ($55 / (1 + r)^2) + ... + ($55 / (1 + r)^11) + ($1000 / (1 + r)^11). Without using the exact formula or a financial calculator, we cannot solve for r directly here, but given the options, a YTM of 7% is reasonable because the bond is selling at a discount (less than its face value), indicating that the YTM should be higher than the coupon rate of 5.5%. Option A is the only one significantly higher than 5.5% and plausible under these conditions.

The Price Perpetual Bank Has Purchased a Bond That Has