Question

6. Assuming that the current interest rate is 3 percent, compute the present value of a five-year, 5 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 4 percent

Answer 1

Part (a) $1,091.60

Part (b) $1,044.52

Step-by-step explanation:

Part (a)

Face Value = FV = $1,000

N = 5 Years

r = YTM = 3%

Coupon Rate = 5%

C = Coupon Payment = 5% x $1,000 = $50

PV = ?? We have to calculate the Present Value

PV = C
`[(1-(1)/((1+r)^(N) ) )/(r)]` +
`(FV)/((1+r)^(N) )`

PV = 50
`[(1-(1)/((1+0.03)^(5) ) )/(0.03)]` +
`(1000)/((1+0.03)^(5) )` = $1,091.60

Part (b)

Now the interest rate changes to 4%

r = 4%

PV = C
`[(1-(1)/((1+r)^(N) ) )/(r)]` +
`(FV)/((1+r)^(N) )`

PV = 50
`[(1-(1)/((1+0.04)^(5) ) )/(0.04)]` +
`(1000)/((1+0.04)^(5) )` = $1,044.52