Question

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 eight years in order 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 a three-bedroom, two-bath house currently costs $275,000. To avoid paying Private Mortgage Insurance (PMI), Stan wanted to make a down payment of 20%.

Because it will be eight years before Stan buys a house, the $275,000 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 was satisfied with this estimation.

Morgan Stanley offers several opportunities for Stan to invest the funds that will be devoted to the purchase of 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 $275,000 home price will grow at 4% per year, what will be the future median home selling price in Round Rock in eight 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 have to be deposited into the Morgan Stanley account (which earns 8% per year) at the end of each month to accumulate the required down payment?

4. If Stan decides to make end-of-the-year deposits into the Morgan Stanley account, how much would these deposits be?

5. If homes in Round Rock appreciate by 6% per year over the next eight years instead of the assumed 4%, how much would Stan have to deposit at the end of each month to make the down payment?

6. If homes in Round Rock appreciate by only 2% per year over the next eight years instead of the assumed 4%, how much would Stan have to deposit at the end of each month to make the down payment?

7. If Stan decided to deposit his down payment funds in less risky certificates of deposit (CDs) earning only 4%, 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.

8. If Stan decided to deposit his down payment funds in a riskier investment of growth stocks that have an expected return of 12%, how much would he have to deposit at the end of each month the make the down payment? Use the down payment needed from number 2 for this calculation.

Answer 1

1. Current cost of house(PV) = $ 275,000

Expected annual growth rate (i) = 4% per year

No. of years (t) = 8

Applying future value formula, FV = PV(1+i)^^t

FV = $275,000 * (1+0.04)^8

= $ 376,356.49

2. Down payment = 20% of the value of the house in the future

= 20% * $376,356.49 = $ 75,271.30

3. Amount at the end of each month = PMT

Required amount (A) = $ 75,271.30

Annual rate of interest ( i) = 8% or 0.08

No. of compounds in an year (n) = 12

No. of years (t) = 8

Applying future value of an annuity formula as stated below,

A = PMT * ( ((1 + i/n)^^nt) – 1) / (i/n)

So, $ 75,271.30 = PMT (((1+0.08/12)^(12*8))-1) / (0.08/12)

$75,271.30 = PMT ( 0.89246 / 0.006667)

$ 75,271.30 = PMT * 133.8686

PMT = $ 75,271.30 / 133.8686

           = $ 562.28

4. Inferring from above that Stan wants to make year-end deposits for down payment due after 8 years,

A = $ 75,271.30

PMT = ?

Rate of interest (i) = 8% or 0.08

No. of years (t) = 8

A = PMT * (((1+i)^^t) – 1))/ i

$75,271.30 = PMT * (((1+0.08)^8)-1) / 0.08

$75,271.30 = PMT * (0.8509/0.08)

PMT = $ 7,076.61