Answer:
Amount An investor lose =$19.9202783
Explanation:
Par value of zero-coupon bond=$1,000
Interest rate at maturity=10%
One year later, increase in interest rate=12%
Required:
How much would an investor lose the first year?
Solution:
Formula:
[tex]FV=PV(1+i)^n[/tex]
In our case:
FV is the par value of bond=$1,000
PV is we have to calculate.
i is the interest rate=10%=0.1
n is the number of years=30 years
[tex]\$1000=PV(1+0.1)^{30}\\PV=\frac{\$1000}{(1+0.1)^{30}} \\PV=\$57.3085533[/tex]
Now after one year:
n will become 29 years
i is 12%=0.12
[tex]\$1000=PV_{later}(1+0.12)^{29}\\PV_{later}=\frac{\$1000}{(1+0.12)^{29}} \\PV_{later}=\$37.383275[/tex]
Amount An investor lose =Amount before increase in IR-Amount after increase in IR
Amount An investor lose = [tex]PV-PV_{later}[/tex]
Amount An investor lose =$57.3085533-$37.388275
Amount An investor lose =$19.9202783
