# Finance Quiz

**QUESTION 1**

Suppose you are planning to purchase a home with a value of $125,000. The bank has offered you a mortgage to finance 80% of the value of the home. How much of your own equity do you need to invest in the purchase of the home?

- $100,000
- $125,000
- $25,000
- $0

**QUESTION 2**

Based on current interest rates, and your credit score, suppose the bank offers you a 30-year, fully-amortizing mortgage with monthly payments at an annual interest rate of 5.47%.

What is your monthly mortgage payment?

- $565.91
- $707.39
- $6,837.50
- $5,470.00

**QUESTION 3**

After ten years, what is the remaining loan balance on the mortgage?

- $53,472.29
- $82,470.58
- $125,618.44
- $98,876.40

**QUESTION 4**

Suppose after ten years, the value of the home has risen from $125,000 to $175,000. At what annualized growth rate has the value of the home grown over the last ten years?

- 2.26%
- 3.42%
- 4.14%
- 40.00%

**QUESTION 5**

Suppose after ten years the value of the house has risen from $125,000 to $175,000. How much equity do you now own in the home?

- $25,000.00
- $92,529.42
- $42,529.42
- $49,381.56

**QUESTION 6**

Suppose you chose to move after ten years, sell your house for $175,000, and pay off the remaining loan balance. What annualized return did you earn on your initial home equity investment?

- 5.46%
- 13.98%
- 2.26%
- 7.04%

**QUESTION 7**

Suppose after you move you purchase a new home. You choose to take out a new mortgage on the new home with an initial loan balance equal to the remaining loan balace on your old home. In this way, you are not borrowing any more or less due to the move, you are just taking out a new loan to pay off the old loan (ignoring any moving expenses and loan closing costs). Suppose you take out a new 30-year mortgage that fully amortizes to zero with monthly payments, but that interest rates have now fallen to 3.17%. What is the monthly payment on your new mortgage? (Note that this situation is equivalent to what happens when interest rates fall and home owners refinance their mortgages at the lower rates)

- $430.83
- $355.31
- $707.39
- $466.71

**Solution**

1) 25000

2) 565.91

3) 82470.58

4) 3.42%

5) 92529.42

6) 13.98%

7) 355.31

**Explanation:**

1) Loan Amount = 125000 * 0.8 = 100000

Own Investment = 125000 * 0.2 = 25000

2) Present Value of Loan = PMT * PVIF(0.4558,360)

100000 = PMT * [ (1 – 1.004558^{-360}) / 0.004558 ]

100000 = PMT * 176.7071

PMT = 100000 / 176.7071

PMT = 565.9082

3) At 10th year Loan outstanding =

Present Value of future Monthly payments = PMT * PVIF(0.4558,240)

= 565.91 * [(1 – 1.004558^{-240}) / 0.004558 ]

= 565.91 * 145.7314

= 82470.58

4) Anual Growth Rate = (175000 / 125000 )^{1/10} – 1

= 1.4^{1/10} – 1

= 1.03422 – 1

= 3.422%

5) Our Equity after 10 Years = 175000 – 82470.58 = 92529.42

6) Annual return on Equity Investment = ( 92529.42 / 25000 )^{1/10} – 1

= 3.70^{1/10} – 1

= 1.1398 – 1

= 13.98%

7) Loan Amount = 82470.58

Present Value of Loan = PMT * PVIF(0.2642,360)

82470.58 = PMT * [ (1 + 1.002642^{-360} ) / 0.002642 ]

82470.58 = PMT * 231.9056

PMT = 82470.58 / 231.9056