The following is the problem that I am working on.
A bank offers an annual interest of 5% per year with continuous interest for 20 yrs. Every year, a person withdraws 12,000 from the account. If the balance equals exactly 0 at the end of the 20th year, what is the principal of the account?
To set up the differential equation is the part that I am not confident.
Intuitively speaking, I know the continuous interest formula would be
and every year the person uses $12,000 from the account so the total usage is
after t years.
So I am thinking that the differential equation should have a solution that looks something like
and to set this equation as a differential equation, I let
But I am not confident if my setup is correct. Can someone lend a hand?