INVESTMENT PLAN An investor makes regular deposits totaling D dollars each year into an account that earns interest at the annual rate r compounded continuously. Explain why the account grows at the rate dV/dt=rV+D where V(t) is the value of the account t years after the initial deposit. Solve this differential equation to express V(t) in terms of r and D. 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? Ray estimates he will need $800,000 to retire. If the prevailing rate of interest is 5% compounded continuously, how large should his regular annual deposits be so that he can retire in 30 years?
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INVESTMENT PLAN An investor makes regular deposits totaling D dollars each year into an account that earns interest at the annual rate r compounded continuously.
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Explain why the account grows at the rate
dV/dt=rV+D
where V(t) is the value of the account t years after the initial deposit. Solve this differential equation to express V(t) in terms of r and D.
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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?
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Ray estimates he will need $800,000 to retire. If the prevailing rate of interest is 5% compounded continuously, how large should his regular annual deposits be so that he can retire in 30 years?
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