3. Suppose a particular person decides to start saving money to buy a house. Suppose they start with an initial balance of y[0] dollars and they invest their money and earn 12% interest per year'. Suppose they supplement their investment with x[n] dollars invested each month immedately following the initial investment (1) Finally, assuming the initial investment is yo = 10,000 dollars and an addi- tional investment of $500 each month, find the account balance across time. To answer this problem, you can simply add your results from parts (e) and (g). Recall that a balance of k dollars at z% interest per year becomes a balance of k(1+z/12/100)" at the end of month n. 2Linear constant coefficient difference equation 6) How many years are required to obtain a $100,000 balance based on the invest- ment strategy in part (1)