After graduating from Ohio State University with a degree in Finance, Kate Myers took a

position as a stock broker with Merrill Lynch in Cleveland. Although she had several college

loans to make payments on, her goal was to set aside funds for the next eight years in order

to make a down payment on a house. After considering the various suburbs of Cleveland, Kate

chose Lakewood as her desired future residency. Based on median house price data, she

learned that a three-bedroom, two-bath house currently costs $300,000. To avoid paying

Private Mortgage Insurance (PMI), Kate wanted to make a down payment of 20%.

Because it will be eight years before Kate buys a house, the $300,000 price will surely not be

the same in the future. To estimate the rate at which the median house price will increase, she

considered the historical price appreciation in Lakewood. In the past, homes appreciated by

nearly 4% per annum. Kate was satisfied with this estimation.

Merrill Lynch provides several opportunities for Kate to invest the funds that will be devoted to

the purchase of her future home. She feels that a balanced account containing stocks, bonds,

and government securities would realistically achieve an annual rate of return of 8%.

Questions

1. Taking into consideration the fact that the $300,000 home price will grow at 4% per

year, what will be the future median home selling price in Lakewood in eight years?

What amount will Kate Myers have to accumulate as a down payment if she does

decide to buy a house in Lakewood?

2. Based on your answer from number 1, how much will have to be deposited into the

Merrill Lynch account (which earns 8% per year) at the end of each month to

accumulate the required down payment?

3. If Kate decides to make end-of-the-year deposits into the Merrill Lynch account, how

much would these deposits be?

4. If homes in Lakewood appreciate by 6% per annum over the next eight years instead

of the assumed 4%, how much would Kate have to deposit at the end of each month

to make the down payment?