Question

Union Local School District has bonds outstanding with a coupon rate of 5.1 percent paid semiannually and 18 years to maturity. The yield to maturity on these bonds is 4.6 percent and the bonds have a par value of $10,000.

  

What is the dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Bond price

$

Answer 1

The dollar price of the bond can be calculated with the help of following formula

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where

Price of the Bond, P0 =?

C = coupon payment or annual interest payment = 5.1% per annum but it makes coupon payments on semiannual basis therefore coupon payment = 5.1%/2 of $10,000 = $255

n = number of payments or time remaining for the maturity of bond = 36 (18*2 for semiannual payments)

i = yield to maturity (YTM) = 4.6% per annum or 2.3% per semiannual

M = value at maturity, or par value = $10,000

Therefore,

Bond Price = $255 * [1 – 1 / (1+2.3%) ^36] /2.3% + 10,000 / (1+2.3%) ^36

= $6197.17 + $4410.39

= $10,607.57

Therefore the price of bond is $10,607.57