1. You have a choice between receiving your salary of $120,000 in equal monthly installments of $10,000 or in a single lump sum at the end of each year. If your required return is 4% p.a. compounding monthly, what year-end salary would you demand?

2. The annual percentage rate (APR) is 10% compounded semi-annually. You are considering purchasing a US Treasury bond that has a face value of $1000, a 4% coupon (nominal rate), and matures in 10 years. Coupons are paid semi-annually and the next coupon payment is exactly six months away.

2.a What is the current price of this bond?

2.b What is the effective annual rate that corresponds to the 10% APR? What is the effective monthly rate?

2.c What is the price of the bond if the next coupon payment is in 3 months, and the bond has 9 years and 9 months to maturity. note: coupons are still paid semi-annually.

3. You are considering taking out a 20 year fixed rate mortgage on a $640,000 house. Current mortgage rates are 3.5% (nominal rate, compounded monthly).

3.a Calculate your monthly payment on this mortgage.

3.b What is the remaining principal after two years (i.e., immediately after the 24th payment)? What are the total interest payments in the first two years?

3.c After exactly two years (i.e., immediately after the 24th payment), you decide to use a $150,000 bonus you received at work to reduce the principal outstanding on your mortgage. You continue making the same monthly payment that was calculated in part (a). When will the loan be fully paid off?

4. You are interested in purchasing a speedboat. The list price is $35,000 and the manufacturer provides financing over eight years at 3.5% p.a. compounding monthly with repayments to be made monthly. One dealer has offered you a $4,500 discount and has offered to provide financing (over eight years) at 5% p.a. compounding monthly with repayments to be made monthly. The question is which terms are more attractive?

5. Ten years ago, a couple purchased a house, financing $260,000 of the purchase with an 6% mortgage (monthly compounded) over 30 years. Interest rates in the market are 3% compounded semi-annually. Today, on the 10th anniversary date of their mortgage (i.e., after they made mortgage payments for 10 years), mortgage rates had fallen to 4%. If they refinance their home at this time with a new 30 year loan, they will incur prepayment penalties and closing costs which together are equal to 5% on the new mortgage. Assume that the couple can finance both the new mortgage and the prepayment penalties and closing costs at the 4% rate. Assume the couple makes monthly payments. Should they refinance their home?

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