Question

(1) A professor contributes $900 per year into a retirement fund by making many small deposits throughut the year. The fund grows at a rate of 9% per year, compounded continuously. After 30 years, the professor retires, and begins withdrawing from the fund at a rate of $2000 per month. If no further deposits are made, how long will the money last? (2 pts each part)

(a) Set up the differential equation that models the situation for putting money into the fund.

(b) Put the DE in (a) into the form of a first order linear DE.

(c) Find an integrating factor to solve the DE

(d) Solve the DE, and use y(0) = 0 as an initial condition to eliminate the arbitrary constant.

(e) Let t = 30 in your solution in part (d) to find how much is in the fund after 30 years.

(f) Set up the differential equation that models the situation for taking money from the fund.

(g) Put the DE in (f) into the form of a first order linear DE.

(h) Find an integrating factor to solve the DE

(i) Solve the DE, and use y(0) = your answer to part (e) as an initial condition to eliminate the arbitrary constant. 2 (j) Let y(t) = 0 to find how long the fund will last. (use Mathematica)

Answer 1