Question

1. Ann gets a 30 year 1/1 Fully Amortizing ARM for $1,000,000, with monthly payments and monthly compounding. The initial rate is 3%. In the future, the rate will reset to 250 basis points above the LIBOR. There are no rate caps or floors. Suppose at the first reset, the LIBOR was 6%. What is the monthly mortgage payment for the second year?

	A.	$4,216.04
	B.	$3,958.47
	C.	$7,585.95
	D.	$7,747.70

2. Sam bought a house that costs $1,000,000. Sam got a 97% LTV loan. The lender demanded that Sam buy private mortgage insurance to insure the portion of the loan over 80% LTV. Suppose 5 years later, Sam’s mortgage balance is $900,000. However Sam defaults and his house sells for $750,000 in a foreclosure auction. How much will the mortgage insurance company pay Sam’s lender?

	A.	$220,000.00
	B.	$170,000.00
	C.	$150,000.00
	D.	$250,000.00

3. A bank makes a 30 year Fully Amortizing, Fixed Rate Mortgage (FRM) for $2,000,000 at an annual interest rate of 4.125% compounded monthly, with monthly payments. What is the market value of this loan after 7 years of payments if the annual interest rate for this loan is 10% compounded monthly?

	A.	$1,045,425.62
	B.	$1,726,113.67
	C.	$ 680,688.05
	D.	$1,101,017.63

4. A bank originates a 30 year Fully Amortizing FRM at an annual interest rate of 5% with monthly compounding and monthly payments. If 10 years later, the bank borrows at 6%, what is this bank’s Net Interest Margin (NIM) on this FRM?

	A.	-11.00%
	B.	-1.00%
	C.	5.00%
	D.	6.00%

5. Ann gets a 30 year 3/1 Fully Amortizing ARM for $1,000,000, with monthly payments and monthly compounding. Ann pays $10,000 in closing costs. The initial rate is 2.50%. In the future, the rate will reset to 250 basis points above the LIBOR. There are no rate caps or floors. Suppose at origination and at the rate reset the LIBOR was 1%.

Part 1: What is the loan balance when the rate resets (round to nearest whole number and enter without commas, e.g. 123,456 enter as 123456)?

Part 2: What is the annualized true APR for the loan (round two decimal places and enter without % sign, e.g. 4.95% enter as 4.95)?

6. A bank makes a 30 year Fully Amortizing FRM for $2,000,000 at an annual interest rate of 4.125% compounded monthly, with monthly payments.Suppose inflation is 2% per year, compounded monthly. What is the real value of the 20th payment?

	A.	$9,050.06
	B.	$9,375.48
	C.	$9,692.99
	D.	$6,523.11

7. Ann got a 30 year Fully Amortizing FRM for $1,000,000 at an annual interest rate of 6% compounded monthly, with monthly payments. After 5 years of payments, Ann can refinance the balance into a 25 year Fully Amortizing FRM at an annual interest rate of 4% compounded monthly, with monthly payments. Refinancing will cost Ann 1 point and $1,500 in closing costs.

If Ann refinances into this loan and makes payments for 25 years, what will be her annualized IRR from refinancing?

	A.	120.36%
	B.	113.09%
	C.	130.05%
	D.	10.03%

8. Ann got a 30 year Fully Amortizing FRM for $1,000,000 at an annual interest rate of 4.25% compounded monthly, with monthly payments. After 5 years of payments, Ann can refinance the balance into a 25 year Fully Amortizing FRM at an annual interest rate of 3.75% compounded monthly, with monthly payments. Refinancing will cost Ann 2 points and $1,500 in closing costs.

If Ann refinances into this loan after 5 years, what will be her total cost of refinancing?

	A.	$19,661.54
	B.	$21,500.00
	C.	$18,161.54
	D.	$20,000.00

9. Which of the following is a reason a borrower may want to refinance?

	A.	The borrower's credit score rises
	B.	The borrower's house value declines
	C.	Lender's demand lower LTVs
	D.	Lender's demand lower DTIs

10. Lucy bought a house for $100,000. Lucy’s annual cost of ownership net of tax savings is exactly equal to the annual rent she would have paid to live in the same house. The house price grows 4.5% annually (compounded annually).

Suppose buying costs are 5% (of the purchase price of the house) and selling costs are 8% (of the selling price of the house). Lucy will sell the house in one year. What is Lucy’s annualized IRR? (hint: it will be negative)

Answer 1

1]

First, we calculate the principal paid off after 1 year (12 months) using CUMPRINC function in Excel :

rate = 3%/12 (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 1000000 (original loan amount)

start period = 1 (We are calculating principal paid off between 1st and 12th month)

end period = 12 (We are calculating principal paid off between 1st and 12th month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be $20,878

The balance loan principal outstanding after 1 year =  $1,000,000 - $20,878 = $979,122

For the 2nd year, the interest rate = LIBOR + margin = 3% + 2.5% = 5.5%

Monthly loan payment is calculated using PMT function in Excel :

rate = 5.5% / 12   (converting annual rate into monthly rate)

nper = 29*12 (29 years remaining on loan with 12 monthly payments each year)

pv = 979122 (balance loan principal outstanding after 1 year)

PMT is calculated to be $7,585.95

The answer is C