You areevaluating two loans for your property. You are looking at purchasing a $$400,000$ property with a $20\%$ downpayment. You can finance this property with either a $30$ year mortgage at a rate of $4\%,$ or a $15$ year mortgage at a rate of $3\mathrm{.}25\%.$ You believe that you have investment opportunities in the stock market that will average a return of $9\%.$

a$)$ What is the payment on the $30$ year mortgage?

b$)$ What is the payment on the $15$ year mortgage?

c$)$ Suppose you take out the $30$ year mortgage, but make the $15$ year payment. First, why would you potentially do this? Second, what will the remaining balance on the $30$ year mortgage be $15$ years from now?

d$)$ If you invest the difference between the $30$ year mortgage payment and the $15$ year mortgage payment in the stock market at the rate indicted, how much will your investment be worth in $15$ years? Is this enough to pay off the mortgage, and does this change our opinion of which option is preferable? Discuss.

e$)$ You don't have to do the calculations for this, but would your analysis change if you had $$20,000$ ni credit card debt that was accruing interest at $18\%?$ Ifso, how?