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1. If you deposit $18 at 18% interest, how much do you have after 18 years if...
   (a) it is simple interest?

      18 ( 1 + (0.18)(18)) = $76.32

   (b) it is compounded yearly?

      18 ( 1 + 0.18 )^18 = $354.12

   (c) it is compounded continuously?

      18 ( exp ( (0.18)(18) ) = $459.61

2. What "effective interest rate" (or "APR") is equivalent to a continuously compounded rate of 5% ?

      exp(0.05)-1 = 0.05127

3 (based on text 4.7). Consider two possible sequences of end-of-year payments. (In each payments are yearly, in dollars, starting at the end of year 1.)
   * 20, 20, 20, 15, 10, 5
   * 10, 10, 15, 20, 20, 20

   a. For what positive interest rates (if any) is the first sequence preferable (to the person who recieves the payments)?

      Any r less than (CORRECTION! GREATER THAN!) about 5.16%

   b. For what positive interest rates (if any) is the second sequence preferable?

      Any r greater than (CORRECTION! LESS THAN!) about 5.16%

   c. How would your answers change (if at all) if the payments started at the beginning of year 1?

      ...no...

4. The remaining payments on an old government bond are as follows: four payments of $1000, at six-month intervals starting six months from now; and one payment of $25,000 exactly two years from now.
   a. If the market risk-free interest rate is 6%, what's the present value of the bond at time 0 ?

      $25886.07

   b. From the information given, can you guess the original coupon rate for the bond?

      Eight percent

5. Suppose that everyone knows (with certainty) that the interest rate is going to remain at 4% from now (time 0) until time 2 years, and then jump suddenly to 6% and stay at 6% forever. (Rates are continuously compounded.)
   a. If you lend $100 at time 0, how much will be in your account at time 3?

      $100 exp(.08) exp(.06) = $115.03

   b. What would you pay at time 0 for the right to receive $1 at time 3? ( That is, what is P(3)? )

      Inverse of 1.1503, which is $0.869

   c. Write a formula for P(t) valid for every t greater than or equal to 0.

      P(t) = exp(-0.04t) if t <= 2 yrs., or
            exp(- (0.08+0.06(t-2)) ) if t >= 2 yrs.

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