A) Suppose you deposite an initial principle of zero in an account paying 6% annual interest compounded continuously. Every year, you make a deposite of K dollars spread out uniformly throughout the year, so that at the end of 25 years the account will have a principle of $50,000. Show that the principle P(t) satisfies the ODE.
dy/dt = 0.06 + K.
B) Find the solution dy/dt = 0.06 + K satisfying P(0)=0. (The as yet unknown constant K will appaer in your formula).
C) Using the formula in B) find the value of K that will meet your objective as stated in A). How much of the final $50,000 consists deposites and how much consists of interest?