Question

A bond will pay $70 of interest at the end of each of the next three years, plus $1,000 at the end of year three. If the present market price is $1,040, its yield-to-maturity is: (a) 5.5%. (b) 4.9%. (c) 6.4%. (d) 6.8%. (e) 7.4%.

Answer 1

Answer:

(a) 5.5%

Explanation:

Yield-to-maturity (YTM) is the discounting rate for calculating the present value of bond & coupon received.

Bond price = Present value of interest received + present value of bond

⇔ 1040 = 70/(1+ YTM)^3+70/(1+ YTM)^2+70/(1+ YTM) + 1000/(1+YTM)3

It's really difficult to solve above equalation, then we try every hint provived.

(a) 5.5% ->True

70/(1+ 5.5%)^3+70/(1+ 5.5%)^2+70/(1+ 5.5%) + 1000/(1+5.5%)^3 = 1040

(b) 4.9%

70/(1+ 4.9%)^3+70/(1+ 4.9%)^2+70/(1+ 4.9%) + 1000/(1+4.9%)^3 = 1057

(c) 6.4%

70/(1+ 6.4%)^3+70/(1+ 6.4%)^2+70/(1+ 6.4%) + 1000/(1+6.4%)^3 = 1016

(d) 6.8%

70/(1+ 6.8%)^3+70/(1+ 6.8%)^2+70/(1+ 6.8%) + 1000/(1+6.8%)^3 = 1005

(e) 7.4%.

70/(1+ 7.4%)^3+70/(1+ 7.4%)^2+70/(1+ 7.4%) + 1000/(1+7.4%)^3 = 990

Answer 2

Answer:

a) 5.5 %

Explanation:

Given FV = $1000, P = $1040, n = 3 YAERS, C = $70, YTM = ?

YTM Formula

= C+F-P/n÷F+P/2

=70+1000-1040/3÷1000+1040/2

=5.5%