Question

What must be the price of a $ 5000 bond with a 6.4​% coupon​ rate, semiannual​ coupons, and two years to maturity if it has a yield to maturity of 8​% ​APR?

Answer 1

Given,

Par value = $5000

Coupon rate = 6.4%

Years to maturity = 2 years

Yield to maturity = 8% or 0.08

Solution :-

Semi annual coupon payment (C) = $5000 x 6.4% x 1/2 = $160

Semi annual periods (n) = 2 years x 2 = 4

Semi annual yield to maturity (r) = 0.08/2 = 0.04

Now,

Price of the bond

= C/r x [1 - (1 + r)^-n] + [par value x (1 + r)^-n]

= $160/0.04 x [1 - (1 + 0.04)^-4] + [$5000 x (1 + 0.04)^-4]

= $4000 x [1 - (1.04)^-4] + [$5000 x (1.04)^-4]

= $4000 x [1 - 0.854804191] + [$5000 x 0.854804191]

= $4000 x 0.145195809 + [$4274.020955]

= $580.783236 + $4274.020955

= $4854.80