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8. You buy a 30-year zero coupon bond which will pay you $10,000 in 30 years at an annual yield of i=1% compounded once per year. A few minutes later the annual yield rises to i=2% compounded once per year. What is the percent change in the value of the bond? (Hint: recall the formula for percent change. The answer should be negative.) 9. You buy a 30 year zero coupon bond which will pay you $1000 in 30 years at an annual yield of i=16.5% compounded once per year. 25 years later it will be a 5 year zero coupon bond. Suppose the interest rate on this bond will be 16.5%, what will the price of this bond be in 25 years?

Respuesta :

Answer:

-74.41%

465.9833221

Explanation:

The computation of percent change in the value of the bond is shown below:-

Price at 1% = $10,000 ÷ 1.01^30

= 7,419.23

Price at 2% = $10,000 ÷ 1.02^30

= 5,520.71

Percentage change in price = 5,520.71 ÷ 7,419.23

= -74.41%

The computation of the price of this bond be in 25 years is shown below:-

Price after 25 years: $1,000 ÷ 1.165^5

= 465.9833221

The percentage change in the value of the bond is 25.6% and the price of the bond in 25 years will be $465.98

Data;

  • Present Value of coupon = $10,000
  • Interest rate = 1%, 2%
  • Time = 30 years.

Percentage Change in the Value of the Bond

This is calculated by the difference between the value of the interest rate.

Value of zero coupon bond = maturity value * PVF (r%, n)

The value of the bond at 1%

[tex]10000* PVF(1\%, 30)\\10000 * 0.7419 = 7,419.23[/tex]

The value of the bond at 2%

Value of zero coupon bond = maturity value * PVF (r%, n)

[tex]10000*PVF(2\%, 30)\\10000*0.5521 = 5521[/tex]

The percentage change is

[tex]\% change = \frac{previous value - present value}{previous value}\\\% change = \frac{7419.23-5521}{7419.23}\\ \% change = 25.6\%[/tex]

The percentage change in the value of the bond is 25.6%

b)

The cost of the zero coupon is equal to the present value of the future cash flow which is discounted at it's rate of interest. The period of discounting is the same as the period which the value needs to be determined.

  • Period = 5 years
  • Rate = 16.5% = 0.165
  • PV = 1000

[tex]p = \frac{1000}{(1+0.165)^2}\\p = 465.98[/tex]

The price of the bond in 25 years will be $465.98

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