Homework SourseA certain bank account contains money you have saved to pay
A certain bank account contains money you have saved to pay for living expenses during retirement. It starts out with 80,000 dollars, and it earns 3.6 percent annual interest compounded continuously. To pay for your living expenses you plan to take out 13,800 dollars every year, which we will assume (for simplicity) is done continuously over the course of each year. If A(t) denotes the amount of money in the account after t years, write down a differential equation satisfied by A(t).
A\'=???
A\'=???
Solution
let at any point of time t, account balance is A(t). then increment in it is given by dA(t)/dt=r*A(t)-K where r=rate of interest=0.036 K=yearly withdrawal=13,800 dollars so integrating dA(t)/[r*A(t)-K]=dt A(t)-(K/r)=c*exp(r*t);c=a constant or A(t)=c*exp(r*t)+383.33*10^3 now A(0)=80000 so c=-303.33*10^3 so A(t)=-303.33*10^3*exp(0.036*t)+383.33*10^3
