Kate MyersBasic Concepts: The Time Value of Money

After graduating from Ohio State University with a degree in Finance, KateMyers took a position as a stock broker with Merrill Lynch in Cleveland.Although she had several college loans to make payments on$,$ her goal wasto set aside funds for the next eight years in order to make a down paymenton a house. After considering the various suburbs of Cleveland, Kate choseLakewood as her desired future residency. Based on median house pricedata, she learned that a three$-$bedroom, two$-$bath house currently costs $$98,000.$ To avoid paying Private Mortgage Insurance $($PMI$).$ Kate wanted tomake a down payment of $20\%.$ Because it will be eight years before Kate buys a house, the $$98,000$ pricewill surely not be the same in the future. To estimate the rate at which themedian house price will increase, she considered the historical priceappreciation in Lakewood. In the past, homes appreciated by nearly $4\%$ perannum. Kate was satisfied with this estimation. Merrill Lynch provides several opportunities for Kate to invest the funds thatwill be devoted to the purchase of her future home. She feels that abalanced account containing stocks, bonds, and government securities wouldrealistically achieve an annual rate of return of $8\%.$

Questions:

Taking into consideration the fact that the $$98,000$ home pricewill grow at $4\%$ per year, what will be the future median home sellingprice in Lakewood in eight years?

What amount will Kate Myers haveto accumulate as a down payment if she does decide to buy a housein Lakewood?$2.$ Based on your answer from number $1,$ how much will have to bedeposited into the Merrill Lynch account $($which earns $8\%$ per year$)$ atthe end of each month to accumulate the required down payment?

If Kate decides to make end$-$of$-$the$-$year deposits into the Merrillynch account, how much would these deposits be$?$ Why is thisamount greater than twelve times the monthly payment amount?

If homes in Lakewood appreciate by $6\%$ per annum over the nexteight years instead of the assumed $4\%,$ how much would Kate haveto deposit at the end of each month to make the down payment? What if the appreciation is only $2\%$ per year?