We wish to calculate the amount of a savings plan for any month, k, given a fixed interest rate, r, compounded monthly. Denote these quantities as follows: uk is the amount in an account at month k, r equals the interest rate compounded monthly, and d equals the monthly deposit. The amount at the end of the next month will be the old amount plus the interest on the old amount plus the deposit. In terms of the above variables this is with a =1+ r/12 and b = d

uk+1 = uk + uk r/12 + d = auk + b.

(a)Use (1.1.2) to determine the amount in the account by depositing $100 each month in an account, which gets 12% compounded monthly, and over time intervals of 30 and 40 years ( 360 and 480 months).

(b) Use a modified version of fofdh.m to calculate and graph the amounts in the account from 0 to 40 years