You purchase a very small 1-bedroom apartment in New York for $1,000,000. You obtain a mortgage with a fixed monthly interest rate, ic = 0.42%/month. You can pay this loan off with a fixed monthly payment of M1, or you can pay a linearly increasing payment, where M2 = b*t.

a. (6 points) Show the principal balances for BOTH the fixed and linearly increasing monthly payment.

b. (8 points) For the FIXED interest rate mortgage, calculate your monthly payment in order to pay the loan off in 30-years.

c. (4 points) For the FIXED monthly payments, calculate the total amount paid on the mortgage after 30 years. 6/7

d. (9 points) For the linearly increasing monthly payment, show the expression for the principal as a function of time, P(t) = ?. Hint: The intergral of ( xe^(ax)) dx = (x/a=1/a^2)e^(ax)

e. (4 points) If the rate of payment increases with a slope of b = $39.52/month, then calculate the principal after 30 years.

f. (4 points) For the linearly increasing monthly payment, calculate the total amount paid on the mortgage after 30 years.