Question

# Q14. Find the yield to maturity of the following securities: A security paying \$1,000 in one...

Q14. Find the yield to maturity of the following securities:

1. A security paying \$1,000 in one year, for which you pay \$926 today.
2. A security paying \$80 one year from now and \$1,080 two years from now, for which you pay \$1,050 today.
3. A security paying \$50 every six months for the next five years (beginning six months from now), plus the return of the face value of \$1,000 at the end of the five years, for which you pay \$1,000 today.

Please include solutions, not the ones already posted (Not correct). Thank you.

1. A security paying \$50 every six months for the next five years (beginning six months from now), plus the return of the face value of \$1,000 at the end of the five years, for which you pay \$1,000 today.

a

 Future value = present value*(1+ rate)^time 1000 = 926*(1+Interest rate/100)^1 Interest rate % = 7.99

b

 K = N Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N k=1 K =2 1050 =∑ [(8*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^2 k=1 YTM% = 5.3

c

 K = Nx2 Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2 k=1 K =5x2 1000 =∑ [(10*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^5x2 k=1 YTM% = 10

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