1. [Balloon Payments]: Audrey Sanborn has just arranged to purchase a $550,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 6.1 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or finance charges. How much will Audrey's balloon payment be in eighty years?
2. [Growing Annuity]: Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $65,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5% of your annual salary in an account that will earn 10% per year. Your salary will increase at 4% per year throughout your career. How much money will you have on the date of your retirement 40 years from today?
3. [Loan Payments] You need a 30 year, fixed-rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at a 5.3% APR for this 360-month loan. However, you can only afford monthly payments of $950, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $950?
4. [Present Value and Break-Even Interest]: Consider a firm with a contract to sell an asset for $115,000 three years from now. The asset costs $76,000 to produce today. Given a relevant discount rate on this asset of 13% per year, will the firm make a profit on this asset? At what rate does the firm just break even?
5. [Variable Interest Rates]: A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 12% compounded monthly for the first seven years, and 6% compounded monthly thereafter, what is the present value of the annuity?
6. [Annuities] You are saving for the college education of your two children. They are two years apart in age; one will begin college 15 years from today and the other will begin l7 years from today. You estimate your children's college expenses to $45,000 per year per child, payable at the beginning of each school year. The annual interest rate is 7.5%. How much money must you deposit in an account each year to fund your children's education? Your deposits begin one year from today. You will make your last deposit when your oldest child enters college. Assume four years of college.