2. You just received a home equity line of credit loan from your bank with an APR (annual percentage rate) of 3.74%, which you plan to use to finance a new roof for your home, a $12,000 expense. However, the bank does not charge its fees annually but monthly, even though you are not required to make any payments for the first year. Let B = the balance (in dollars) of your loan account after m months. (a) What will your monthly interest rate be? (b) Write down a formula for B in terms of m. Then use it to determine what the balance in the account will be at the end of the year, assuming that you make no payments. Subtract the original loan amount of $12,000 to discover how much you are paying for the loan in the first year if you make no payments. (e) Lett - time measured in years; write down a formula that gives m in terms of t, then substitute this into the formula for B to obtain an exponential formula for B in the form B = a. (d) The percentage rate of change indicated by the growth factor in the formula from part (c) is called the annual percentage yield, or APY. It describes the effective in- terest rate for financing your loan due to monthly compounding, so it will be larger than the APR. Determine the APY for this loan