A bond with 20 years remaining until maturity is currently trading for 111 per 100 of par value. The bond offers a 5% coupon rate with interest paid semi-annually. The bond's Annual yield-to-maturity is closest to:
A) 2.09%.
B) 4.18%.
C) 4.50%.

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payment:
Coupon payment = (5% * $100) / 2 = $2.50

Next, we need to calculate the present value of the bond's coupon payments:
PV of coupon payments = ($2.50 / (1 + (y/2))) + ($2.50 / (1 + (y/2))^2) + ... + ($2.50 / (1 + (y/2))^40)

where y = yield-to-maturity

Using a financial calculator or spreadsheet program, we can solve for y by setting the present value of the bond equal to its current market price:

PV of bond = ($2.50 / (1 + (y/2))) + ($2.50 / (1 + (y/2))^2) + ... + ($2.50 / (1 + (y/2))^40) + ($100 / (1 + (y/2))^40)= $111

We find that the closest answer choice is B) 4.18%.

A Bond with 20 Years Remaining Until Maturity Is Currently