An investor makes regular deposits totaling D dollars each year into an account that earns interest at the annual rate r compounded continuously.

a. Explain why the account grows at the rate

where V(t) is the value of the account t years after the initial deposit. Solve this separable differential equation to find V(t). Your answer will involve r and D.

b. Amanda wants to retire in 20 years. To build up a retirement fund, she makes regular annual deposits of $8,000. If the prevailing interest rate stays constant at 4% compounded continuously, how much will she have in her account at the end of the 20-year period?

c. Anibal estimates that he will need $800,000 to retire. If the prevailing annual rate of interest is 5% compounded continuously, how large should his regular annual deposits be so that he can retire in 30 years?

Transcribed Image Text:

dV dt = rV + D