Real Estate Finance Quizzes (with chart)

A borrower takes out a 30-year fully amortizing CPM loan for $250,000 with an interest rate of 5%. What would the monthly payment be? a. $1,342 b. $1,355 c. $1,042 d. $694

a. $1,342 PV= - 250000; I/Y=5/12; N=30*12=360; FV=0; PMT= ? 1,342

What is the present value (PV) of a loan that calls for the payment of $1000 per year for three years if the annual discount rate is 5 percent and the first payment will be made one year from now? a. $2,723.25 b. $2,150.00 c. $3,152.50 d. $2,857.14

a. $2,723.25 PMT = -1000; N=3; I/Y=5; FV=0; PV=? 2,723.25

An interest-only mortgage is made for $80,000 at 10% interest for 10 years. The lender and borrower agree that monthly payments will be constant and will require no loan amortization. If the loan is repaid after five years, what will be the yield to the lender? a. 10% b. 8.25% c. 10.47% d. 9.57%

a. 10% Because this is an interest-only mortgage, no amortization happens.As such, the yield to the lender is the same as the interest rate=10%. Monthly payments for interest-only loan = monthly interest rate * loan amount =( 10%/12) * 80000= 666.67 N = 12x5 = 60 PMT = -$666.67 PV = $80,000 FV = -$80,000 Solve for the annual yield: I/Y = 0.83333 ===> annual yield = 0.83333% (x12) = 10%

A borrower takes out a 30-year mortgage loan for $100,000 with an interest rate of 6% plus 4 points. What is the effective cost of borrowing rate on the loan if the loan is carried for all 30 years? a. 6.4% b. 6.0% c. 5.6% d. 6.6%

a. 6.4% First, calculate monthly payment: PV=-100,000; N=360; I/Y=6/12; FV=0; PMT=? 599.55 Second, calculate effective annual interest rate: Since points are paid up front, the borrowers actually receives less than the face value. Amount received= loan amount - points paid = 100,000- 100,000* 4%= 96000. In order to calculate the effective cost of borrowing rate, we need to use the amount received as the present value, thus: PV=-96000; N=360; PMT=599.55; FV=0; I/Y=? 0.53 <===this is monthly level interest rate, we need to multiply by 12 to get annual rate %So, effective cost of borrowing rate: 0.53%*12=6.4%

Use the following information to answer questions 9 through 10. A borrower takes out a 30-year price level adjusted mortgage loan for $200,000 with monthly payments. The initial interest rate is 4% with 4 points. Assuming that inflation is expected to increase at the rate of 3% for the next 5 years, and a fully amortizing loan is made. What is the monthly payment in year 2? a. 983.48 b. 954.83 c. 966.16 d. 938.02

a. 983.48 Look at Chart 1 at the top of the page

Which of the following is false? a. A major benefit of a PLAM is the mortgage payment increases closely following borrower salary increases b.One difference between the constant amortizing mortgage (CAM) and the constant payment mortgage (CPM) is the interest paid and loan amortization relationship. With a CAM, the loan amortization and interest paid are directly related and with the CPM the loan amortization and the interest paid are inversely related c. Borrowers with fixed rate mortgages generally benefit if actual inflation is higher than expected inflation d. With a reverse mortgage the borrower receives payments from the bank

a. A major benefit of a PLAM is the mortgage payment increases closely following borrower salary increases

Which of the following is false? a. Callable loans are callable at the borrower's option. b.One difference between the constant amortizing mortgage (CAM) and the constant payment mortgage (CPM) is the interest paid and loan amortization relationship. With a CAM, the loan amortization and interest paid are directly related and with the CPM the loan amortization and the interest paid are inversely related. c. Borrowers with fixed rate mortgages generally benefit if actual inflation is higher than expected inflation. d. Lenders and investors worry about default, inflation, legislative, and liquidity risks

a. Callable loans are callable at the borrower's option.

Which of the following is false? a. Determining a loan balance on a CPM is a simple future value of an annuity problem b. Borrowers with fixed rate mortgages generally benefit if actual inflation is higher than expected inflation c. A borrower takes out a 30-year mortgage loan for $250,000 with an interest rate of 5% and monthly payments. $1,125 of the first month's payment would be applied to interest d. The loanable funds theory states that interest rates are a function of the supply of and demand for loanable funds

a. Determining a loan balance on a CPM is a simple future value of an annuity problem

Which of the following is false? a. For reverse mortgage loans, borrowers take all the interest rate risk. b. For CAM loans, lenders take all the interest rate risk. c. For CPM loans, lenders take all the interest rate risk. d. For PLAM loans, lenders and borrowers share the interest rate risk.

a. For reverse mortgage loans, borrowers take all the interest rate risk.

Which of the following is true? a. If the inflation is expected to increase, the increase in payments for a PLAM loan continues over the life of the loan even though loan amortization begins to occur as the number of remaining years to maturity declines b. On the day of origination, the initial interest rate and expected yield for all ARMs should be the same as that of a FRM c. Discount points decrease the lender's effective loan yield d. Negative amortization reduces the principal balance of a loan

a. If the inflation is expected to increase, the increase in payments for a PLAM loan continues over the life of the loan even though loan amortization begins to occur as the number of remaining years to maturity declines

Which of the following is false: a. The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually. b. The future value of $1,000 compounded quarterly for 8 years at 12% may be calculated with the following formula: FV = $1,000 * (1 + 3%)32 . c. Simple interest only earns interest on the principal of the initial investment. d. Given other things being equal, the future value of $800 deposited today would be greater if that deposit earned 8% rather than 7.75% .

a. The future value of a $1 annuity compounded at 5% annually is greater than the future value of a $1 annuity compounded at 5% semi-annually.

Which of the following is a disadvantage of PLAMs? a. The price level used to index PLAMs is measured on an ex post basis and historic prices may not be an accurate reflection of future price b. A PLAM is the mortgage payment increases closely following borrower salary increases c. Lenders face high levels of interest rate risk under PLAMs d. If an unanticipated rise in inflation occurs after the PLAM loan has been made, lenders can lose substantial value

a. The price level used to index PLAMs is measured on an ex post basis and historic prices may not be an accurate reflection of future price

A borrower has a 30-year fully amortizing mortgage loan for $200,000 with an interest rate of 6% and monthly payments. If she wants to pay off the loan after 8 years, what would be the outstanding balance on the loan? a. $91,246 b. $175,545 c. $84,886 d. $146,667

b. $175,545 First, calculate the monthly payment if the loan is fully amortized in 30 years. FV=0; PV=- 200,000 I/Y=6/12; N=30*12=360; PMT=? 1199.10 Second, calculate the loan balance if the loan is repaid in 8 years: PV=200,000 PMT= - 1199.10; N=8*12=96 I/Y=6/12 Solve for mortgage balance: FV=? 175,545

Your friend just won the lottery. He has a choice of receiving $50,000 a year for the next 20 years or a lump sum today. The lottery uses a 15% discount rate. What would be the lump sum your friend would receive? a. $316,426.23 b. $312,966.57 c. $1,000,000.00 d. $500,000.00

b. $312,966.57 PMT = -50000; N=20; I/Y=15; FV=0; PV=? 312,967

A partially amortizing CPM loan is made for $60,000 for a term of 10 years. The borrower and lender agree that a balance of $20,000 will remain and be repaid as lump sum at maturity date. If the interest rate is 7%, what must monthly payments be over the 10-year period? a. $812.20 b. $581.10 c. $696.65 d. $666.67

b. $581.10 N=10x12 or 120 I/Y = 7%/12 or 0.58 PV = -$60,000 FV = $20,000 Solve for monthly payment: PMT = $581.10

A bank makes a $50,000 loan and will receive payments of $600 each month for 20 years as repayment. What is the rate of return to the bank for making this loan? a. 1.12% b. 13.4% c. 10.92% d. 0.91%

b. 13.4% PV=50,000; PMT = -600; N=20 * 12=240; FV =0; I/Y=? 1.12% ===> Annual rate = 1.12% *12 =13.4%

A fully amortizing CPM loan is made for $100,000 at 6.5% interest. If the monthly payments are $1,000 per month, when will the loan be repaid? Assume no prepayment. a. 101 months b. 145 months c. 144 months d. 100 months

b. 145 months Solution: n (PMT,i,PV,FV) i/y = 6.5/12 PMT = - $1,000 PV = $100,000 FV = 0 Solve for maturity: N = 144.42 ==> The loan will be repaid in 145 months.

Which of the following is false? a. The accrual rate is usually the nominal rate divided by the number of periods within a year that will be used to calculate interest. b. APR stands for accrued percentage rate. c. Negative amortization means that the loan balance owed increases over time because payments are less than interest due. d. Partial amortization occurs when payments exceed interest due but not by enough to reduce the amount owed to zero at maturity.

b. APR stands for accrued percentage rate

Which of the following is false? a. ARMs help lenders combat unanticipated inflation changes, interest rate changes, and a maturity gap b. ARMs eliminate all the lender's interest rate risk c. Lender's can partially avoid estimating interest rates by tying an ARM to an interest rate index d. A margin is a component of an ARM

b. ARMs eliminate all the lender's interest rate risk

Assuming all APRs equal, the effective interest rate on a loan is highest when: a. The loan has no points and a 30 year maturity and is prepaid in five years b. Points are charged and the loan has a 30 year maturity but prepaid in five years c. Points are charged and the loan is paid off at maturity in 30 years d. The loan has no points and is prepaid at maturity

b. Points are charged and the loan has a 30 year maturity but prepaid in five years

Which of the following statements is false? a. Effective borrowing cost is different from the APR because the latter is calculated assuming that the loan is repaid at maturity. b. Repaying a loan early always affects the actual or true interest cost to the borrower. c. Effective borrowing cost is different from the contract rate because it includes financing fees (points, origination). d. Nominal rate of interest on a mortgage loan is usually quoted as an annual rate, however the time intervals used to accrue interest is generally not quoted explicitly.

b. Repaying a loan early always affects the actual or true interest cost to the borrower.

Which of the following statements is false? a. if the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series b. for a given discount rate, the present value of a future sum decreases as the number of discounting periods per year decreases c. the present value of a future sum decreases as the discount rate increases d. if the present value of a sum is equal to its future value, the interest rate must be zero

b. for a given discount rate, the present value of a future sum decreases as the number of discounting periods per year decreases

In comparison to the first month's payment of a CAM, the first month's payment of a CPM: a. Cannot be determined with this information b. Is lower c. Is the same d. Is higher

b. is lower

A borrower takes out a 30-year fully amortizing mortgage loan for $500,000 with an interest rate of 12% and monthly payments. What is the accrued interest amount as of the end of the first month? What is the effective annual rate of interest? a. $5,143.06; 12% b. $5,000; 12% c. $5,000;12.68% d. $5,143; 12.68%

c. $5,000;12.68% Accrued interest amount = Accrued interest rate * loan balance = (12%/12)* 500,000 = 5000; Effective annual rate of interest (EAR) = (1+(APR/12))12 -1= (1+12%/12) 12 -1 =1.0112 -1 = 1.12683 - 1=0.12683=12.68%

Determine the present value (PV) if $10,000 is to be received at the end of five years and the discount rate is 5% with semiannual compounding. a. $7,835.26 b. $6,139.13 c. $7,811.98 d. $8,838.54

c. $7,811.98 FV=- 10000; N=5*2=10; PMT=0; I/Y=5/2; PV=? 7,811.98

A borrower takes out a 30-year mortgage loan for $100,000 with an interest rate of 6% plus 4 points. What is the effective cost of borrowing rate on the loan if the loan is repaid after 10 years? (Choose the nearest number) a. 8.1% b. 6.2% c. 6.6% d. 7.4%

c. 6.6% First, calculate monthly payment: PV= - 100,000; N=360; I/Y=6/12; FV=0; PMT=? 599.55 Second, calculate the loan balance: PV=100,000; I/Y=6/12; N=12*10=120; PMT= -599.55 Mortgage balance: FV=? 83685.81 Third, calculate the effective annual interest rate if the loan is repaid in 10 years: Since points are paid up front, the borrowers actually receives less than the face value. Amount received= loan amount - points paid = 100,000- 100,000* 4%= 96000. In order to calculate the effective cost of borrowing rate, we need to use the amount received as the present value, thus: PV=100,000(1-4%)=96000; N=10*12=120; PMT=-599.55; FV=-83685.81; I/Y=? 0.55<===this is monthly level interest rate, we need to multiply by 12 to get annual rate So, the effective cost of borrowing rate if the loan is repaid in 10 years: 0.55%*12=6.6%

A fully amortizing mortgage CPM loan is made for $100,000 at 12% interest for 30 years. Payments are to be made monthly. What would the breakdown of interest and principal be during month 20? (Choose the nearest value) a. 1029; 115 b. 1010; 19 c. 994.; 35 d. 998; 31

c. 944;35 First, calculate monthly payment: PV=100,000; N=360; I/Y=12/12; FV=0; == > PMT=-1028.61 Second, calculate the loan balance at the end of month 19: PV=100,000; I/Y=12/12; N=19; PMT= -1028.61 Mortgage balance by the end of month 19: FV=? 99404.60 Mortgage balance by the end of month 19 = loan balance at the beginning of month 20 Third, calculate interest payment: Interest payment in month 20=monthly interest rate * loan balance at the beginning of month 20= (12%/12)*99404.60=994.05 Fourth, calculate principal payment: Principal payment during month 20=monthly payment - interest payment of month 20=1028.61 - 994.05 =34.56

Which of the following is true? a. For a fully amortizing CPM loan, its amortization is constant overtime. b. Inflation makes very little difference to lenders of and investors needing money. c. For a fully amortizing CPM loan, its loan balance is reduced only very slightly at first. d. For a fully amortizing CPM loan, its interest payment is increasing overtime.

c. For a fully amortizing CPM loan, its loan balance is reduced only very slightly at first.

At the end of five years, calculating the loan balance of a constant payment mortgage is simply the: a. Future value of an ordinary annuity b. Future value of a single amount c. Present value of an ordinary annuity d. Present value of a single amount

c. Present value of an ordinary annuity

___________ is(are) adjusted for inflation. a. The interest rate of PLAM loans b. The discount points of PLAM loans c. The loan balance of PLAM loans d. The origination fees of PLAM loans

c. The loan balance of PLAM loans

An interest-only mortgage is made for $80,000 at 10% interest for 10 years. The lender and borrower agree that monthly payments will be constant and will require no loan amortization. What will the monthly payments be? What will be the loan balance after five years? a. $666.67; 0 b. $800.00; 80,000 c. $8,000; 0 d. $666.67; 80,000

d. $666.67; 80,000 Monthly payments for interest-only loan = monthly interest rate * loan amount =( 10%/12) * 80000= 666.67 Because this is an interest-only mortgage, no amortization happens. As such, the loan balance after five years is still 80,000. PV=80,000 PMT= -666.67 I/Y=10/12; N=5*12=60; Solve for mortgage balance: FV=? 80,000

A fully amortizing mortgage loan is made for $100,000 at 6% interest for 20 years. Assume the loan is repaid at the end of eight years. What will be the outstanding balance? How much total interest will have been collected by then? (Choose the nearest value) a. $89,256.55; $68,777.28 b. $73,416.24; $68,777.28 c. $89,256.55; $42,193.50 d. $73,416.24; $42,193.50

d. $73,416.24; $42,193.50 First, calculate the monthly payment if loan is fully amortized in 20 years: FV=0; PV=-100,000 I/Y=6/12; N=20*12=240 PMT=? 716.43 Second, calculate the loan balance if the loan is repaid in 8 years: N=8*12=96 I/Y=6/12 PMT=-$716.43 PV=$100,000 Solve for mortgage balance: FV=$73,416.22 Total interest collected by the end of year 8: = total payment + mortgage balance - principal $716.43 x (8 x 12) + $73,416.22 - 100,000 = $42,193.50

The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent compounded quarterly is a. $ 17,549 b. $ 11,200 c. $ 93,049 d. $ 75,401

d. $75,401 PMT = -1000; N=4*10=40; PV=0; I/Y=12/4=3; ==> FV=? 75,401.26

You have recently seen a credit card advertisement that states that the annual percentage rate (APR) is 20 percent. If the credit card requires monthly payments, what is the effective annual rate of interest on the loan? a. 20.00% b. 23.45% c. 18.22% d. 21.94%

d. 21.94% EAR=(1+(APR/12))12 - 1 = (1+(20%/12))12 - 1=1.0166712 - 1=1.21939 - 1 =0.21939 =21.94%

Your subscription to Consumer Reports is about to expire. You may renew it for $24 a year or, instead, you may get a lifetime subscription to the magazine for a onetime payment of $400 today. Payments for the regular subscription are made at the end of each year. Using a discount rate of 5%, how many years does it take to make the lifetime subscription the better deal? a. 36 years b. 35 years c. 34 years d. 37 years

d. 37 years PMT = -24; FV=0; I/Y=5; PV= -400; N=? 36.72 ==> It takes 37 years to make the lifetime subscription the better deal.

A widow wishes to take out a reverse mortgage on her house. What annual payment can she get if she decides on a $100,000 debt at the end of 10 years, the current rate is 9%, and she wants to take a $10,000 advance? (Choose the nearest value) a. $1,558 b. $5,924 c. $1,402 d. $5,024

d. 5,024 PV=10,000; I/Y=9, N=10,== > FV=23673.64 Future value of advance = $10,000 *1.0910= $23,674 $100,000 - 23,674 = $76,326 available for annuity FV=76,326, I/Y=9; N=10; PV=0; == > Annual Annuity = PMT=? 5,024

What is the expected effective yield to the lender if the loan is repaid in 2 years? (Choose the nearest number) a. 12% b. 7% c. 6% d. 9%

d. 9% Look at Chart 2 at the top of the page CF0= - 200,000 (1-4%)= - 192,000 CF1= 954.83; n=12 CF2= 983.48; n=11 CF3=983.48+204,555=205538.48; n=1 IRR = 0.75 Annualize it : 0.75%*12=9%

Which of the following descriptions most accurately reflects the risk position of an ARM lender in comparison to that of a FRM lender? Interest Rate Risk Default Risk a. Lower Lower b. Higher Lower c. Higher Higher d. Lower Higher

d. lower, higher

The future value of a single deposit of $1,000 will be greater when this amount is compounded: a. Semi-annually b. Annually c. Quarterly d. Monthly

d. monthly

Which of the following is not one of the major components in the mortgage interest rate? a. the prepayment risk premium b. the inflation premium c. the real rate of interest d. the Institutional risk premium

d. the Institutional risk premium