## Question

1) While vacationing, Harry Rogers saw the vacation home of his dreams. It was listed with a sale price of $200,000. The only catch is that Harry is 40 years old and plans to continue working until he is 65. Still, he believes that prices generally

increase at the overall rate of inflation. Harry believes that he can earn 9% annually after taxes on his investments. He is willing to invest a fixed amount at the end of each of the next 25 years to fund the cash purchase of such a house (one that can be purchases today for $200,000)

a) Inflation is expected to average 5% per year for the next 25 years. What will Harry’s dream house cost when he retires?

b) How much must Harry invest at the end of each of the next 25 years to have the cash purchase price when he retires?

2) You are about to buy your first home. You will take out a $300,000 mortgage for 30 years, monthly payments, with a fixed rate of 6%

a) What is your monthly payment?

1) How much of that payment will be applied to interest?

2) How much will be applied to the principle?

b) What will your total payments be over the entire 30 year period?

1) How much of that total will be interest?

2) How much will be principle?

c) What will be the outstanding loan balance after 10 years?

d) During that 10 year period, what were your total payments?

1) How much of that total will be interest?

2) How much will be principle?

e) What will be the outstanding loan balance after 20 years?

f) During that 20 year period, what were your total payments?

1) How much of that total will be interest?

2) How much will be principle?

3) A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate 4 years later. Currently, the annual cost (for everything – food, clothing, tuition, books, transportation and so forth) is $15,000, but these costs are expected to increase by 5% annually. The college requires that this amount be paid at the start of the year. She now has $7,500 in a college savings account that pays 6% annually. Her father will make six equal annual deposits into her account; the first deposit today and the sixth on the day she starts college. How large must each of the six payments be? (Hint: Calculate the cost (inflated at 5%) for each year of college and find the total present value of those costs, discounted at 6%, as of the day she enters college. Then find the compounded value of her initial $7,500 on that same day. The difference between the PV of these costs and the amount that would be in her savings account must be made up by the father’s deposits, so find the six equal payments (starting immediately) that will compound to the required amount.

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