Getting a job 1) Assume you earn $30,000 annually on your first job after gradua

ID: 2449506 • Letter: G

Question

Getting a job

1) Assume you earn $30,000 annually on your first job after graduation. Assume you receive a $5,000 raise after your first year on the job. Thereafter, you receive 5% raises annually. how much money will you be earning after five years on the job? (What will be your annual salary at the beginning of your sixth year?)

Buying a House

2) After you've been working five years, you decide to buy a house. As a rule of thumb, your house payments should not exceed 25% of your gross pay. Based on your annual salary during your sixth year on the job, what is the maximum amount you could afford in the house payments per year?

3) Calculate the maximum house payment you could afford per month?

4) Assume you will qualify for an 8%, 30-year conventional mortgage. How much could you borrow based on the maximum monthly payment you can afford? (8% compounded monthly)

5) Lenders often expect that you have 20% of the value of the house as a down payment. Assume that you will be able to make a 20% down payment. What is a total cost of the house you could afford? The total cost is equal to the mortgage plus the down payment. (HINT: Use algebra. You want to calculate 20% of the value of the house, not 20% of the amount you are financing.)

Explanation / Answer

1) Annual salary at the start is $30,000. After first year, there is a raise of $5,000 and from 2nd year it is 5% annually. So here is your annual earnings

Year

Salary

Increase

Total (Salary +Increase)

$30,000

$5,000

$35,000

$35,000 * 5% = $1,750

$36,750

$36,750 * 5% = $1,837.50

$38,587.50

$38,587.50 *5% = $1,929.38

$40,156.88

The annual salary at the beginning of the 6th year will be $ 40,156.88 (Rounded off to 2 decimals)

2) The house payments should not exceed 25% of your gross pay. The Gross pay in the 6thyear as calculated is $40,156.88. Based on that maximum amount you could afford in the house payments per year is

$40,156.88 * 25% = $10,129.22

3) Maximum house payment you could afford per month will be

$10,129.22/12 = $844.10 (rounded off to 2 decimals)

4) Maximum amount that can be afforded per month as per the question 3 is $844.10. So if you take 30 years conventional mortgage loan, maximum amount you will be able to pay in 30 years is $844.10 * 12 * 30 = $ 303,876.00

It is given that interest rate is 8% and compounded monthly. Using the monthly compound interest formula, we have to calculate the loan amount.

P = A / (1 + r/n) ^ nt.

= $303,876/ (1+0.08/12) ^ (12 *30)

= $303,876/ (1+0.08/12) ^ 360

= $303,876/ (1+0.006667) ^ 360

= $303,876/ 10.93703 (Note: 1.006667 to the power of 360 value is calculated using scientific calculator)

= $27,784.14

So with the monthly payment you could afford, the amount you can borrow is $27,784.14 for 8% interest compounded monthly, 30-year conventional mortgage.

5) From question 4 above we know the amount of loan we can borrow. It is given that 20% of the value of the house will be made as down payment. So for the 80% of the value of the house we have to take mortgage.

Mortgage amount we could take is $ 27,784.14. This is 80% of the value of the house. So the total cost of the house you could afford is

$27,784.14 / 80% = $34,730.18 (Rounded off to 2 decimals)