Problem 10 Sarah and John have $60,000 raised in 4 years. are saving money for a

Question

Problem 10 Sarah and John have $60,000 raised in 4 years. are saving money for a down payment on a house. They are hoping to (A) How much do they they would like in 4 years? need to deposit now, at 6% compounded continuously, to have the amount (B) How much interest will have been earned? (C) Assuming they can only deposit $15,000 now, with the above interest rate, how much more will they need to complete the $60,000 after 4 years? (D) Suppose they can deposit $15,000 now, at what interest rate would they be able to accumulate the entire $60,000 in 4 years, assuming continuous compounding?

Explanation / Answer

a. A = P ert

    60000 = P e0.06*4

    60000 = P e0.24

   P = $47918

B. Interest = Amount, A- Principle,P = 60000-47918 =$12082

C . Let the extra invested amount be x

     60000 = (15000+x) e0.06*4

    15000 +x = 47918

     x = 47918 -15000 = $32918

D . 60000 = 15000 e4r

     4 = e4r

4r = ln 4

r = 0.3466

r = 34.66 %

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