Problem 1 Suppose you want to buy a house for $420,000 and you have $40,000 in savings you can use as a down payment. The rest you finance with a 5-year mortgage (monthly payments) with a quoted interest rate of 5.34% (APR). 1 Assume that this mortgage is amortized over 25 years. a) What are the monthly payments over the 5-year term of the mortgage? b) How much do you still owe three years after you took out this mortgage (i.e., immediately after you made the 36th monthly payment)? c) What is the principal portion of the 37th mortgage payment? d) What would be the bi-weekly payments (you would make payments once every two weeks) if you switched to bi-weekly payments right after you made the 36th monthly payment. Assume there is no penalty for switching and that the effective interest rate remains the same. Also assume that you would make bi-weekly payments for the remainder of the term, i.e., 22 years, and that a year has exactly 52 weeks. e) Suppose your bank offers you a car loan with a monthly compounded APR of 5.34%. Which of the two loans is cheaper: the mortgage or the car loan? Or are you paying the same effective interest rate on both?

Problem 2 You have just won the lottery and you can choose between the following payout options. The annual interest rate (EAR) is 10%. a) $100,000 right now and $60,000 every two years starting 4 years from now and ending 16 years from now (i.e., payments are at t = 0, t = 4, t = 6, , t = 14, t = 16). b) $60,000 a year for 20 years with the first payment one year from today (i.e., payments are at t = 1, 2, 3 19, 20). c) 25 annual payments of $45,000 and a 26th payment of $299,000. The first payment is made right now, and the $299,000 payment is made two years after the last $45,000 payment. How much more is the best option worth today relative to the worst option?

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