Question

YIELD TO MATURITY AND FUTURE PRICE

A bond has a $1,000 par value, 10 years to maturity, and a 7% annual coupon and sells for $985.

1. What is its yield to maturity (YTM)? Round your answer to two decimal places.
   
      %
   

2. Assume that the yield to maturity remains constant for the next 2 years. What will the price be 2 years from today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

a. Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods-10

r-YTM-

Face value or par value =1000

Coupon payment=Coupon rate*face value=7%*1000=70

Putting values in formula

985=70*((1-(1/(1+r)^10))/r)+1000/(1+r)^10

Solving we get r-YTM=7.2157%

Thus YTM=7.22%(Rounded off)

b. After 2 years

n-8(Years to maturity)

Putting values in formula of price of bond

Price of bond=70*((1-(1/(1+.072157)^8))/.072157)+1000/(1+.072157)^8

Solving we get price of bond=$987.23