Question

You find a zero coupon bond with a par value of $25,000 and 18 years to maturity.

If the yield to maturity on this bond is 3.9 percent, what is the dollar price of the bond? Assume semiannual compounding periods.

What is the bond price?

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 this is zero coupon bond, so there will be no interest payments.

The bond payment at maturity is a one time payment, so we will use the formula for present value (PV) of $1. The interest rate that will be used in calculating the required present values will be the semi annual interest rate, which is 3.9% /2 = 1.95%, with 18*2 = 36 periods.

Now,

Bond price = PV (1.95%, 36 years)

The formula for present value of $1 is :

PV = C / (1 + r)ⁿ

where, C is the value of bond at maturity = $25000, r is the rate of interest = 1.95%, and n is the time period = 36

Putting these values in the above formula, we get,

PV = $25000 / (1 + 1.95%)³⁶

PV = $25000 / ( 1 + 0.0195)³⁶

PV = $25000 / (1.0195)³⁶

PV = $25000 / 2.00419642957

PV = $12473.83

So, price of the bond is $12473.83