Question

A bond with a face value of $1000 makes quarterly payments of $20. The bond is currently selling for $1047.83 and has 10 years remaining until maturity. What is the bond's official yield-to-maturity? Write your answer out to four decimals - for example, write 6.18% as .0618.

Answer 1

Face Value =1000

Quarterly Coupon Amount =$20

Bonds value or price =1047.83

Years to Maturity = 10

Number of Quarterly periods (n)= 10*4= 40

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

I is that rate at which Bond price is Equal to Actual price of 1047.83

Here i is Quarterly rate.

Assume i is 1.70%

Bond price = 20*(1-(1/(1+1.7%)^40))/1.7% + 1000/(1+1.7%)^40

=1086.55516

Assume i = 1.9%

Bond price =20*(1-(1/(1+1.9%)^40))/1.9% + 1000/(1+1.9%)^40

=1027.841436

interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))
=1.7% +((1.9%-1.7%)*(1086.55516-1047.83)/(1086.55516-1027.841436))

=0.01831911783

Annual or official Yield to Maturity = Quarterly rate*number of quarters in year

=0.0183*4

=0.0732 or 7.32%

So official Yield to Maturity is 7.32%