Question

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.

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.

Answer 1

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