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 10% yield to maturity, only to see market interest rates increase to 12% one year later?

Answer 1

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:

$FV=PV(1+i)^n$

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

$\ 1000=PV(1+0.1)^{30}\\PV=\frac{\ 1000}{(1+0.1)^{30}} \\PV=\ 57.3085533$

Now after one year:

n will become 29 years

i is 12%=0.12

$\ 1000=PV_{later}(1+0.12)^{29}\\PV_{later}=\frac{\ 1000}{(1+0.12)^{29}} \\PV_{later}=\ 37.383275$

Amount An investor lose =Amount before increase in IR-Amount after increase in IR

Amount An investor lose = $PV-PV_{later}$

Amount An investor lose =$57.3085533-$37.388275

Amount An investor lose =$19.9202783