# solution

Consider the following sequence of cash flows. Pay \$500 today and \$100 in
exactly 2 years in exchange for receiving payments of \$200 one year from today
and \$500 three years from today.
(a) Write the present value of these cashflows as a function of the annual
effective interest rate i.
(b) Compute the modified duration for this sequence of cashflows when i = 4%.
(c) Compute the modified convexity when i = 4%.
(d) Use the second order modified approximation to find the approximate
present value if the interest rate falls by 30 basis points.
(e) Compute the Macaulay duration and convexity when i = 4%.
(f) Use the second order Macaulay approximation to find the approximate
present value if the interest rate falls by 30 basis points.
(g) Find the exact present value of these cashflows if the interest rate falls by
30 basis points.
(h) Compare the errors in the modified and Macaulay approximations in this
case

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