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 0.07. 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 3376000 dollars in 47 years?

d=

Explanation / Answer

A(t) = d + d(1 + i) +d(1 +i)^2 + ........ +d(1 + i)^t this above relation is obtained by adding the final amount contributed by each individual years deposits d = final deposit d(1+i) = deposit before the final one ...... d(1+i)^t = the very first deposit hence A(t) = d ((1+i)^(t+1) - 1)/i cant ask multiple questions or bits here post them in some other question i will help you for sure......:)

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