After graduating from the University of Texas with a degree in Finance, Stan Morgan took a position as a stockbroker

with Morgan Stanley in Austin. Although he had several college loans to make payments on$,$ his goal was to set aside

funds for the next ten $(10)$ years to make a down payment on a house. After considering the various suburbs of Austin,

Stan chose Round Rock as his desired future residency. Based on median house price data, he learned that three$-$bedroom,

two$-$bath houses currently have a median price of $$450,000.$ To avoid paying Private Mortgage Insurance $($PMI$),$ Stan

wanted to make a down payment of $20\%.$

Because it will be ten years before Stan buys a house, the $$450,000$ price will surely not be the same in the future. To

estimate the rate at which the median house price will increase, he considered the historical price appreciation in Round

Rock. In the past, homes appreciated by $4\%$ per year. Stan decided to use this estimation in his calculations.

Morgan Stanley offers several opportunities for Stan to invest the funds that will be devoted to the down payment toward

his future home. He feels that a balanced account of stocks, bonds, and government securities would realistically achieve

an annual rate of return of $8\%.$

Questions:

$1.$ Taking into consideration that the $$450,000$ median home price will grow at $4\%$ per year, what will be the future

median home selling price in Round Rock in ten years?

$2.$ Based on your answer from number $1,$ what amount will Stan Morgan have to accumulate as a down payment if

he does decide to buy a house in Round Rock?

$3.$ Based on your answer from number $2,$ how much will Stan need to deposit into the Morgan Stanley balanced

account $($which earns $8\%$ per year$)$ at the end of each month to accumulate the required down payment?

$4.$ If Stan decides to make deposits once a year $($at the end of each year$)$ deposits into the Morgan Stanley account,

how much would these deposits be$?$

$5.$ Take your answer from number $3$ and multiply it by $12$ to determine Stan$$s total deposits per year when making

$12$ monthly deposits. Compare that to your end$-$of$-$year deposit answer from number $4.$ Explain why Stan$$s total

deposits per year $($when making $12$ monthly deposits$)$ is less than when making one annual deposit per year.

$6.$ If homes in Round Rock appreciate by $6\%$ per year over the next ten years instead of the assumed $4\%,$ what is

Stan$$s revised needed down payment and how much would Stan have to deposit at the end of each month to make

that down payment?

$7.$ If homes in Round Rock appreciate by only $2\%$ per year over the next ten years instead of the assumed $4\%,$ what

is Stan$$s revised needed down payment and how much would Stan have to deposit at the end of each month to

make the down payment?

$8.$ If Stan decided to deposit his down payment funds in less risky low$-$growth investments earning only $4\%$ instead

of $8\%,$ how much would he have to deposit at the end of each month to make the down payment? Use the down

payment needed from number $2$ for this calculation.

a$.$ If Stan decides to make deposits once per year at the end of the year into this less$-$risky account, how

much would these deposits be$?$

$9.$ If Stan decided to deposit his down payment funds in riskier high$-$growth investments earning a return of $12\%$

$($instead of $8\%),$ how much would he have to deposit at the end of each month to make the down payment? Use

the down payment needed from number $2$ for this calculation.

a$.$ If Stan decides to make deposits once per year at the end of the year into this riskier account, how much

would these deposits be$?$

$10.$ Based on your calculations, should Stan make end of month or end of year deposits? Why?

$11.$ Based on this information, do you recommend he deposit his funds in the balanced account with $8\%$ expected

return, the low growth, less risky, investments with $4\%$ expected return, or the high growth, riskier, investments

with $12\%$ expected return? Why?