A retiree deposits S dollars into an account that earns interest at an annual rate r compounded continuously, and annually withdraws W dollars.

a. Explain why the account changes at the rate

where V(t) is the value of the account t years after the account is started. Solve this separable differential equation to find V(t). Your answer will involve r, W, and S.

b. Frank and Jessie Jones deposit $500,000 in an account that pays 5% interest compounded continuously. If they withdraw $50,000 annually, what is their account worth at the end of 10 years?

c. What annual amount W can the couple in part (b) withdraw if their goal is to keep their account unchanged at $500,000?

d. If the couple in part (b) decide to withdraw $80,000 annually, how long does it take to exhaust their account?

Transcribed Image Text:

dV dt = rV - W