Question

Question 5 Compare a two-year bond with two successive one-year bonds, in which an investor buys a one-year bond today, then another one-year bond when the first matures. Suppose the two-year bond has an annual interest rate of 8 percent. Consider the pattern of interest rates on the one-year bonds listed below and explain whether an investor should buy the two-year bond or the one-year bond today. In each case, how much would an investor have at the end of two years if the investor invested $25,000 today? Show your work.

(a) The interest rate on a one-year bond today is 6 percent; and the interest rate on a one-year bond purchased one-year from now is 9 per cent.

(b) The interest rate on a one-year bond today is 10 percent; and the interest rate on a one-year bond purchased one-year from now is 7 per cent.

Answer 1

Solution:

If an investor invested in a two year bond at the rate of 8 percent, they would earn 29160 dollars over two years.

Total Sum = Principal(25000) + Interest

{Interest = Principal(25000)*Rate(8%)*Time(2 years)}

(a)

R (Year 1) = 6%

R(Year 2) = 9%

Total Sum earned at end of Y1 = Principal(25000) + Interest(25000*0.6*1)

Total Sum = 26500

Total Sum earned at end of Y2 =Principal(26500) +Interest(26500*0.9*1)

Total Sum = 28885

Therefore the investor should invest in the two year bond since 29160 is greater than 28885.

(ii)R(Year 1) = 10%

R(Year 2) = 7%

Use the same formula to calculate the total sum at the end of two years which comes out to be 29425 dollars.

Therefore the investor should invest in two one year bonds since 29425 is greater thaan 29160.

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