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Suppose the term structure of risk-free interest rates is as shown below: Term (years) 1 2 3 4 5 Rate 1
Suppose the term structure of risk-free interest rates is as shown below:
| Term (years) | 1 | 2 | 3 | 4 | 5 |
| Rate | 1.99% | 2.22% | 2.74% | 3.03% | 3.33% |
a. Calculate the present value of an investment that pays $1000 in two years and $2000 in five years for certain.
Answer: the present value is ____ $. (round to two decimals)
b. Calculate the present value of an investment that pays $100 at the end of each of year from 1 to 5 for certain.
Answer: the present value is ____ $. (round to two decimals)
c. If you wanted to value the investment in b. correctly using the annuity formula, which discount rate (%) should you use?
Answer: the discount rate is ___ %. (round to three decimals)
(Hint: value correctly means that the present value of payments using the annuity formula equals the PV that has been computed in b.)
d. What is the shape of the yield curve given the term structure in the Table above?
Answer: Yield curve is _____ . (fill in "increasing" or decreasing")
Expert Solution
1.
=1000/1.0222^2+2000/1.0333^5=2654.8801908447
2.
=100/1.0199+100/1.0222^2+100/1.0274^3+100/1.0303^4+100/1.0333^5=459.600601211774
3.
=RATE(5,-100,100/1.0199+100/1.0222^2+100/1.0274^3+100/1.0303^4+100/1.0333^5)=2.87570235003283%
4.
Increasing
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