Section 2: Applications. 7. An investor deposits $5000 in an account that earns

Question

Section 2: Applications. 7. An investor deposits $5000 in an account that earns 6.5% interest compounded quarterly. a. Determine how much money will be in the account 10 years after making the initial investment b. Determine how many years it will take for the investor to double his original investment. c. The investor could have chosen to invest the money in an account that earns 6% interest compounded continuously. In that case, how long would it have taken for him to double his original investment? Which interest rate is the better investment?

Explanation / Answer

7. a. A(t) =A (1+r/n)nt

             =   5000(1+0.065/4)4*10 = Approx $9528

   b. Double of 5000 = 10000

      10000 = 5000(1+0.065/4)4t

       2   = (4.065/4)4t

      log 2 = 4t log(4.065/4)

       t =10.75 years

c.   A(t) = A ert

      10000 = 5000 e0.065t

      ln 2 = 0.065 t

     t=10.66 years

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