Question

8. You buy a zero-coupon bond which will pay you $1000 in 30 years. Annual discount rate is i= 6% compounded once per year. A few minutes later the discount rate rises to i= 7%. What is the percent change in the value of the bond? Hint: if an answer is negative, do not drop the minus sign.

9. You buy a zero-coupon bond which will pay you $1000 in 30 years. Annual discount rate is i= 14% compounded once per year. What will be the price of this bond 25 years later? Suppose the discount rate stays the same.

Answer 1

Price of Zero coupon bond= F/(1+i)^n

Where

F= Face value, i= interest rate and n= period

Q#8:

Given,

F= $1,000.   Interest rate (on purchase)= 6% Interest rate after change= 7% and n= 30 years

Plugging the values,

Price at which the bond is bought (P0)= 1000/(1+6%)^30 = 1000/ 5.743491173 = $174.11

Price after increase in interest rate (P1)= 1000/(1+7%)^30 = 1000/ 7.612255043 = $131.37

Percentage change= [(P1-P0)/P0]*100 = [(131.37-174.11)/174.11]*100

= (-42.74/174.11)*100 = -24.5494%

Q#9:

Given,

F= $1,000.   Interest rate = 14% Period at the time of purchase ( n)= 30 years and period afterwards= 30-25 =5 years

Plugging the values,

Price of the bond after 25 years= 1000/(1+14%)^5

= 1000/ 1.925414582 = $519.37