You will be investing money into a bank account that earns 4 percent annual inte

Question

You will be investing money into a bank account that earns 4 percent annual interest, compounded continuously. You plan to invest dollars into the account every year. You are saving for retirement, and you want to have 400,000 dollars in the account after 20 years.

A'= (A*.04)+R

B) Assuming there is no money in the account at time t=0, give a formula for A(t). (Do this by solving the initial value problem. Your answer will still have the undetermined constant R in it. )

A(t)=??

C) What should R be in order to meet the goal of having 400,000 dollars in the account after twenty years?

R=??

Explanation / Answer

dA/dt =.04A +R

or, dA/(.04A+R)=dt

or, (1/.04)ln(.04A+R)=t+d (d=constant)

or, .04A=Cet/25-R (C=constant)

or, A=25(Cet/25-R)

at t=0, A=0

So, 0=25(Ce0-R) or, C=R

So, A=25R(et/25-1) (ans to B)

at t=20, A=400000

So, 400000=25R(e20/25-1)

or, 400000=25R(1.23)

or, R=13008.13

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