Question

How much would an investor lose the first year if she purchased a 30-year zero-coupon bond with a $1,000 par value and a 9.5% yield to maturity, only to see market interest rates increase to 11% one year later?

Answer 1

Sol:

Par value (FV) = $1000

Period (n) = 30 years

Yield to maturity (r) = 9.5% in first year, After 1 year 11%

To determine how much investor will lose in the first year:

Present value (PV) at year zero with 9.5% rate = FV / ( 1 + r)^n

Present value (PV) at year zero = 1000 / ( 1 + 9.5%)^30

Present value (PV) at year zero = 1000 / ( 1.095)^30

Present value (PV) at year zero = $65.70

Present value (PV) at year 29th with 11% rate = FV / ( 1 + r)^n

Present value (PV) at year 29th with 11% rate = 1000 / ( 1 + 11%)^29

Present value (PV) at year 29th with 11% rate = 1000 / ( 1.11)^29

Present value (PV) at year 29th with 11% rate = 48.49

Amount investor lose in the first year = $65.90 - $48.49 = $17.41

Therefore amount investor lose in the first year will be $17.41