You decide to plan for retirement and begin to put 12 monthly payments each year into an interest-bearing account. The account earns interest at an annual interest rate of R % compounded continuously (for calculations, we use r = R 100 ). If you put A0 dollars initially (at t = 0) into the account and make payments of D dollars per month thereafter, the amount of money in the account A(t) at time t > 0 (t is measured in years) is given by the solution to the following IVP for A(t):

A 0 (t) = rA(t) + 12D

A(0) = A0

Solve the IVP to find the particular solution in terms of the parameters A0, r and D. This will give you a function that you can use to determine the answers to part (b). SHOW ALL WORK!