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

Amount An investor lose =$19.9202783

Step-by-step 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=(\$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)=(\$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