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1. The Rule of 72. People like to say that if you invest money at constant r% interest, then it doubles in N years where rN = 72. (Or, equivalently, N = 72/r.) For example, if you invest at 12%, your money doubles in 6 years. This is obviously an approximation, but it's a pretty good one.

First, look at the text, Example 4.1d (pp. 40-41) to see why this works. (The text wants to use 70 in place of 72, but it's more fun to divide numbers into 72.)

   a. Do this part in your head in 30 seconds or less: If you invest $100 at a constant 6% interest rate, approximately how much do you have after 24 years?

   b. Now calculate it more accurately, assuming that the interest is compounded continuously (that is, using ert). Are you happy with your estimate in part a?

2. Suppose that the present value curve is given by P(t) = exp(-0.11 t), for all t >= 0. Using the notation from the text, section 4.4,
   a. What is D(t) ?
   b. What is r(s) (the forward interest rate curve) ?
   c. What is the yield curve ? (That's r(t) with a bar over the r, but I can't type it right in html.)

3. Now suppose that P(t) = 1 / (1+t2) (sorry for the typography; t2 means t squared) for all t >= 0.
   a. What is D(t) ?
   b. What is r(s) ?
   c. What is the yield curve ? (It's ok to write (c) as an integral; you don't need to evaluate the integral.)

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