Show all work. Label and clearly explain your answer.

1) Gordon Barbara wishes to purchase a mansion in Gotham City.To do so, she will have to borrow 12 million dollars.The market interest rate is 0.50% per month.

a) Suppose Gordon takes a 30-year loan with equal monthly payments.What will be the amount of the monthly payments?

b) Suppose instead, Gordon takes a 90-year loan with equal monthly payments. What will be the amount of the monthly payments?

c) Now suppose that Gordon takes a 90-year loan with equal monthly payments, as in (b).Further, suppose that 30 years from now, market interest rates drop to 0.25% per month. Gordon decides to refinance and takes out a 60-year loan.What will be the amount of the new payments?

2) Bryce Wayne has recently inherited $90 million dollars.He estimates that his monthly living expenses will be $100,000 per month for thirty years. He also plans to make the following one-time future expenditures.

1) He wishes to purchase a mansion next year for four million dollars.

2) He wishes to purchase and remodel a cave to use as his laboratory and fortress.

He plans to purchase the cave in 5 years and forecasts that the cost will be ten million dollars.

Bryce would also like to fund his favorite charity, by giving monthly contributions to the Society for the Prevention of Cruelty to Bats.He would donate a fixed amount of money per month (starting next month) in perpetuity.How much could Bryce donate per month, while making sure he has enough money to cover his expenses and planned expenditures? The appropriate interest rate is 0.33% monthly.