Question

You own a bond that pays $64 in interest annually. The face value is $1,000 and the current market price is $1,062.50. The bond matures in 30 years. What is the yield to maturity? (round your answer to two decimal places)

Answer 1

Calculating Yield to Maturity,

Using TVM Calculation,

I = [PV = -1,062.50, FV = 1,000, PMT = 64, N = 30]

I = 5.95%

Answer 2

Bond price = 1062.50

Face value = 1000

Annual Coupon = 64

Years to Maturity (n)= 30

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

1062.50= (64*(1-(1/(1+i)^30))/i) + (1000/(1+i)^30)

I is that rate at which Bond Price is 1062.50

i will be calculated by trial and error method and interpolation Formula

Assume i is 5.50%

Bond Price = (64*(1-(1/(1+5.5%)^30))/5.5%) + (1000/(1+5.5%)^30)

=1130.803707

Assume i is 6%

Bond Price = (64*(1-(1/(1+6%)^30))/6%) + (1000/(1+6%)^30)

=1055.059325

interpolation formula for rate calcuy = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))

=5.5% +((6%-5.5%)*(1130.803707-1062.50)/(1130.803707-1055.059325))

=0.05950882991 or 5.95%

So Yield to Maturity is 5.95%