(3) Suppose we are saving up money in an account with a yearly interest rate of 4% (compounded continuously). We will start with an initial deposit of $30,000
(a) Without any extra deposit, how much money do we expect to have in the account after 5 years?
(b) Now suppose you make constant yearly deposits of $2,000. Write down an IVP that models this problem, find its solution and estimate how much money we will have in the account after 5 years.
(c) Now suppose you are willing to increase the amount you deposit every year, calling this new fixed amount D. What is the smallest value for D be so that in 5 years we will have more than $50,000 in our account?