A young person with no initial capital invests d dollars per year in a retiremen

Question

A young person with no initial capital invests d dollars per year in a retirement account at an annual rate of return 0.04. Assume that investments are made continuously and that the return is compounded continuously. Let A(t) be the amount of money in the account after t years.

A. Write down a differential equation for A(t) :

A? =
[Hint: Ask yourself how much money is being added to the account each year.]

B. Solve the differential equation and determine a formula for A(t), assuming A(0)=0. The only unknown constant in your answer should be d.

A(t)=

C. What value of d will provide 3213000 dollars in 44 years?
d =

Explanation / Answer

Let d is the amount he invests into the account per year- from formula- A=Pe^(rt), A(t) = d e^( 0.04t) A. dA/dt = d x e^( 0.04t) x 0.04

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