Question

You have a $1000 par value bond with a current bond price of $900 and a semiannual coupon of $50. If the YTM on this bond is 10% (compounded semiannually), how many years are there until maturity

Answer 1

Answer:

2.22 years

Explanation:

Face value = $ 1000

Current bond price = $900

YTM = (5%*2) = 10%

Coupon payment = (1,000 * 10%/2) = $50

YTM =  C + [(F − P)/n] / [(F + P)/2]

0.05 * 2 = {50 + (1000 - 900/ n)} / {1000 + 900 / 2}

0.10 = {50 + (1000 - 900/ n)} / 950

0.10 * 950 = {50 + (1000 - 900/ n)}

95 = 50 + (100 / n)

95 = (50n + 100) / n

95n = 50n + 100

95n - 50n = 100

45n = 100

n = 100/45

n = 2.22222

Thus, the years to maturity = 2.22 years