Let us know if you got a helpful answer. Question Suppose that a risk-neutral in
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Suppose that a risk-neutral investor has a choice between buying a one-year bond paying 4 percent today, a two-year bond paying 5 percent today, a three-year bond paying 5.3 percent today, or a four-year bond paying 5.8 percent today, if a one-year bond purchased one year from now is expected to have an interest rate of 5.5 percent, a one-year bond purchased two years from now is expected to have an interest rate of 6 percent, and a one-year bond purchased three years from now is expected to have an interest rate of 7 percent. If the investor has a 4 year time horizon, which combination would the investor buy? To receive full credit, you must show all calculations.
*** Please show how the yields for the combinations are calculated!
Explanation / Answer
Assuming $100 par value bond used for the calculations and also assuming that interest rate is annually compounding.
Formula used for compound interest is A=P(1+r/100)n
A is the maturity proceeds.
P is the principal amount
r is the rate of interst
n is the number of periods of interst calculation.
For calculation of maturity proceeds of reinvestment after one year, the maturity proceeds of one year bond is used, for calculation of maturity proceeds of reinvestment after two years, maturity proceeds of two year bond is used, for calculation of maturity proceeds of reinvestment after three years, maturity proceeds of three year bond is used.
The results are tabulated as below:
For calculation of maturity proceeds of reinvestment after one year, the maturity proceeds of one year bond is used, for calculation of maturity proceeds of reinvestment after two years, maturity proceeds of two year bond is used, for calculation of maturity proceeds of reinvestment after three years, maturity proceeds of three year bond is used.
From the above calculation, the investor is receiving more amount if he is investing in the bond that matures after 4 years. The yields of all the combinations are less than the different combinations. Hence, the investor should straight away invest in a 4 year bond compounding annually.
Particulars 1 year bond 2 Year bond 3 Year bond 4 Year bond Interest rate 4% 5% 5.3% 5.8% Par value of the bond 100 100 100 100 Maturity proceeds 104 110.25 116.75759 125.29758 Interest rate After one year After two years After three years One Year bond interest rates 5.5% 6% 7% Reinvestment done After one year After two years After three years Maturity proceeds 109.72 116.865 124.93062Related Questions
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