Question

you find a zero-coupon bond with a par value of $10,000 abd 15 years to maturity. if the yield to maturity on the bond is 6%, what is the price of the bond?

Answer 1

Price of the bond can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Since it is a zero coupon bond, so there will be no interest / coupon payments. So, present value of interest payments will be zero.

Next, we will calculate the present value of bond payment at maturity:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)n

where, FV = Future value = $10000, PV = Present value, r = rate of interest = 6%, n= time period = 15

now, putting theses values in the above equation, we get,

$10000 = PV * (1 + 6%)15

$10000 = PV * (1 + 0.06)15

$10000 = PV * (1.06)15

$10000= PV * 2.3965581931

PV = $10000 / 2.19163693671

PV = $4172.65

So, price of the bond is $4172.65