To a difference equation of the form y_k+1 ^_ ay_k = b, for suitable constants a and b. At time k = 0, an initial investment of $1000 is made into a savings account that pays 6% interest per year compounded monthly. (The interest rate per month is .005.) Each month after the initial investment, an additional $200 is added to the account. For k = 0, 1, 2,...,let yk be the amount in the account at time k, just after a deposit has been made.

a. Write a difference equation satisfied by {yk}. 

b. Create a table showing k and the total amount in the savings account at month k, for k = 0 through 60. List your program or the keystrokes you used to create the table. 

c. How much will be in the account after two years (that is, 24 months), four years, and five years? How much of the five-year total is interest?