Math (Loan-to-Value/Gross debt service ratio)

Question 1

A property is listed for $133,333 but the market value, as estimated in a recent appraisal is $125,000. The property’s lending value is estimated to be $120,000. Jay and Joan purchase the home for $128,500 subject to a mortgage of $84,000.

What loan-to-value ratio was applied by the lender with whom Jay and Joan negotiated the mortgage? (Assume that the loan-to-value ratio was the binding constraint on the loan size.)

(1) 67.5%
(2) 70%
(3) 72%
(4) 75%

Answer 1

2

84,000(mortgage) / 120,000 (lending value)
=.70

Question 2

What will be the maximum loan granted on a commercial building with a lending value of $3,500,000 and yielding a net operating income of $360,000 per year, where the lender requires a debt coverage ratio of 1.25 and an 80% loan-to-value ratio. The loan will be amortized over 20 years with annual payments and the interest rate is 7.5% per annum, compounded annually. Round your answer to the nearest $1,000.

(1) $2,936,000
(2) $2,800,000
(3) $3,036,000
(4) $2,590,000

Answer 2

2

80% X 3,500,000
=2,800,000.00

VS

360,000/1.25

j1 = 7.5
n=20

? -288,000 0

=2,936,013.51

the lower amount is..

2,800,000.00

Question 3

Douglas Maxwell, a prospective home buyer, has applied for a mortgage loan to finance the purchase of a townhouse listed at $176,000. The market value of the townhouse is $175,000 and the lender has assigned a $170,000 lending value to it. The lender requires a loan-to-value ratio of 80%. Calculate the maximum loan allowable under the lender’s loan-to-value ratio constraint.

(1) $136,000
(2) $140,800
(3) $139,000
(4) $127,000

Answer 3

1

lending value
170,000X 80%
=136,000

Question 4

Corey has offered $431,000 for a house, providing he is able to obtain acceptable financing. The house lists for $442,000, but the lender has determined the lending value is $440,000. The lender requires a loan-to- value ratio of 80% and a gross debt service ratio of 32%. Property taxes are $2,750 per year and Corey’s annual gross income is $75,000.

If the interest rate is 6% per annum, compounded semi-annually, the amortization period is 20 years, and payments are made monthly, what is the maximum amount this lender will advance, rounded to the nearest
$10?

(1) $352,000
(2) $230,530
(3) $248,650
(4) $320,640

Answer 4

3

.32 = pmt + 2,750
_________
75,000

=24,000-2750=21250.00 /12 = 1770.83 monthly payment

j2 = 6%
n=240

? -1770.83 0

=250,367.57

80% X 440,000 = 352,000.00

answer = 250,367.57

Question 5

The selling price of a property is $175,000. The buyer has applied to a lender for mortgage funds and been told that the maximum loan he can obtain is $122,500. The lender’s appraiser feels that a long-term conservative estimate of the property’s value is $153,125. Which one of the following statements is TRUE?

(1) The lending value of this property is $122,500.
(2) The lending value of this property is $175,000.
(3) The loan-to-value ratio on this loan is 70%.
(4) The loan-to-value ratio on this loan is 80%.

Answer 5

4

i dont really get this one but the equation is

122,500/153,125 = .80 %

i think what they are saying is that the 153,125 is the lending value of the home

Question 6

An individual is planning to purchase a property that has a list price of $69,000. The proposed purchase price will be $67,000 and the lender will apply a lending value of $66,000. How large will the down payment be if the lender insists on a maximum loan-to-value ratio of 80%?

(1) $14,200
(2) $16,500
(3) $50,250
(4) $52,800

Answer 6

1

this one is surprisingly tricky

first need to determine the max mortgage which is

66,000 (lending value) X 80%
=52,800.00

then you need to subtract 52,800 from the purchase price 67,000

=14,200.00

Question 7

Norm Abrahm has offered $231,000 for a house, providing he is able to obtain acceptable financing. The house lists for $242,000, but the lender has appraised the house at $238,000. The lender requires a loan-to- value ratio of 80% and a gross debt service ratio of 28%. Property taxes are $1,750 per year and Mr. Abrahm’s annual gross income is $85,000.

If the interest rate is 12% per annum, compounded annually, the amortization period is 15 years, and payments are made monthly, what is the maximum amount this lender will advance, rounded to the nearest
$10?

(1) $143,250
(2) $178,500
(3) $158,270
(4) $190,400

Answer 7

3

.28(gdsr) = PMT + 1,750
__________
85,000

=22,05.00 DIVIDED BY 12 = 1,837.50 (payment)

J1 = 12%
n=15(180)

? -1,837.50 0

=158,270.45

vs

238,000 X 80% = 190,400.00

lower value wins which is

$158,270

Question 8

Jake Touche wants to purchase a house that is listed for $276,000. The bank’s appraiser estimates that the lending value of the property is $275,000. Jake’s gross annual income is approximately $50,000 per year. The bank applies a 80% loan-to-value ratio and a gross debt service ratio of 32%. Property taxes amount to $1,800 per year. Assume that the lender demands a 25-year amortization period and monthly payments at j2 = 5%. How much can Jake borrow, rounded to the nearest $10?

(1) $220,000
(2) $195,600
(3) $216,360
(4) $203,460

Answer 8

4

275,000 X .80
=220,000.00 (max lending value)

.32 = pmt + 1,800
_________
50,000

=16,000-1800/12
=1,183.33

j2 = 5%
n = 25

? -1,183.33 0

=$203,460

Question 9

A property is listed for $488,888, but the property’s lending value is estimated to be $480,000. Jay and Joan purchase the home for $485,500 subject to mortgage of $360,000.

What loan-to-value ratio was applied by the lender with whom Jay and Joan negotiated the mortgage? (Assume that the loan-to-value ratio was the binding constraint on the loan size.)

(1) 67.5%
(2) 70%
(3) 72%
(4) 75%

Answer 9

4

morgage amount 360,000 divided by lending value (480,000)
= 75%

Question 10

An individual is planning to purchase a property that has a list price of $368,888. The proposed purchase price will be $365,000 and the lender will apply a lending value of $363,000. How large will the down payment need to be if the lender insists on a maximum loan-to-value ratio of 80%?

(1) $74,600
(2) $73,000
(3) $75,300
(4) $76,888

Answer 10

1

this one caught me off guard,
ok,

first figure out the loan amount
80% X lending value ( 363,000)
=290,400.00

then take the purchase price
365,000 - 290,400.00
=74,600.00

Question 11

Mr. Singh has offered $331,000 for a house, providing he is able to obtain acceptable financing. The house lists for $342,000, but the lender has set the lending value at $338,000. The lender requires a loan-to-value ratio of 80% and a gross debt service ratio of 30%. Property taxes are $2,800 per year and Mr. Singh’s annual gross income is $80,000.

If the interest rate is 5% per annum, compounded semi-annually, the amortization period is 20 years, and payments are made monthly, what is the maximum amount this lender will advance, rounded to the nearest
$100?

(1) $270,400
(2) $293,700
(3) $255,600
(4) $268,800

Answer 11

4

Question 12

Joe and Sue Mortgagor wish to purchase a house. Joe’s annual gross income is $35,000 and Sue’s annual gross income is $30,000. The house they wish to purchase has a price of $210,000. Ripley Finance Company has told the Mortgagors that they can supply uninsured mortgage funds for the house at j2 = 7.5%, with an amortization of 25 years and monthly payments. They have determined that the house has a lending value of $208,000, and annual property taxes are $1,900. Ripley uses a policy of requiring a 30% gross debt service ratio and will lend to a maximum of 80% loan-to-value. In the calculation of gross income, Ripley includes 100% of the principal wage-earner’s income, and 75% of the secondary wage earner’s income. Calculate the maximum loan the Mortgagors can expect (rounded to the nearest dollar).

(1) $174,856
(2) $166,400
(3) $208,000
(4) $150,006

Answer 12

2

208,000X 80%
=166,400

VS

.30 = pmt + 1,900
__________
57,500

j2 = 7.5%
n=25(300)

? 1,279.16 0

=174,854.95

lesser amount is ..

$166,400

Question 13

The selling price of a property is $350,000. The purchaser has applied to a lender for mortgage funds and been told that the maximum loan he can obtain is $268,000. The lender’s appraiser feels that a long-term conservative estimate of the property’s value is $335,000. What is the loan-to-value ratio on this loan?

(1) 77%
(2) 75%
(3) 80%
(4) 70%

Answer 13

2

appears to be 268,000/350,000
=.76

Question 14

A borrower approaches Ripley Finance Company about a mortgage on an income-producing property. The property produces an annual net operating income of $112,500. The lending value of the property is
$880,000. Ripley will only lend to a maximum of 80% loan-to-value ratio, and requires a minimum debt coverage ratio of 1.25. Ripley’s terms are: j12 = 12%, a term and amortization period of 15 years, and monthly payments. Given these constraints, calculate the maximum allowable loan (rounded to the nearest dollar).

(1) $624,912
(2) $660,000
(3) $976,426
(4) $634,728

Answer 14

1

boom!
ok first
880,000X 80% = $704,000

112,500(net operating income)/1.25 (we remembered this part now!)

remember the 1.25 is a RATIO! not a percentage%

90,000/12 monthly payments = 7,500

j12=12%
n=15 (180)

? -7,500.00 0

=$624,912

Question 15

Ryan wants to purchase a house that is listed for $376,000. The bank’s appraiser estimates that the lending value of the property is $370,000. Ryan’s gross income is $75,000 per year. The bank applies a 80% loan-to-value ratio and a gross debt service ratio of 30%. Property taxes amount to
$2,200 per year. Assume that the lender demands a 25-year amortization period and monthly payments at j2 = 8%. How much can Ryan borrow, rounded to the nearest dollar?

(1) $296,000
(2) $221,651
(3) $172,953
(4) $224,387

Answer 15

2

370,000 X 80% = 296,000

VS

30% = PMT + 2,200
___________
75,000

20,300/12 = 1,691.66

j2 = 8%
n=300

? -1,691.66 0

Question 16

What will be the maximum loan granted on a commercial building with a lending value of $4,250,000 and yielding a net operating income of $212,500 per year, where the lender requires a debt coverage ratio of 1.3 and a 65% loan-to-value ratio. The loan will be amortized over 25 years with annual payments and the interest rate is 6.5% per annum, compounded annually. Round your answer to the nearest $1,000.

(1) $1,994,000
(2) $2,997,000
(3) $1,592,000
(4) $2,762,500

Answer 16

1

4250,000X 65%=2,762,500.00

212,500/1.3

j1 = 6.5
n= 25

? -163,461 0

=$1,993,877.12

Question 17

What will be the maximum loan granted on a commercial building with a lending value of $5,550,000 and yielding a net operating income of $360,000 per year, where the lender requires a debt coverage ratio of 1.35 and a 60% loan-to-value ratio. The loan will be amortized over 20 years with annual payments and the interest rate is 7% per annum, compounded annually. Round your answer to the nearest $1,000.

(1) $2,814,000
(2) $3,330,000
(3) $3,592,000
(4) $2,825,000

Answer 17

4
we getting good now!

60% X 5,550,000 = 3,330,000.00

vs

360,000/1.35 = 266,666.66

j1 = 7%
n=20
? -266,666.66 0

=2,825,070

Question 18

Allison Gunther, a prospective home buyer, has applied for a mortgage loan to finance the purchase of a townhouse listed at $276,000. The market value of the townhouse is $275,000 and the lender has assigned a $270,000 lending value to it. The lender requires a loan-to-value ratio of 80%. Calculate the maximum loan allowable under the lender’s loan-to-value ratio constraint.

(1) $220,000
(2) $216,000
(3) $221,000
(4) $225,000

Answer 18

2

270,000 X 80%
=216,000

Question 19

A property is listed for $133,333 but the market value, as estimated in a recent appraisal, is $127,500. The property’s lending value is estimated to be $120,000. Jay and Joan purchase the home for $128,500 subject to mortgage of $84,000.

What loan to value ratio was applied by the lender with whom Jay and Joan negotiated the mortgage? (Assume that the loan to value ratio was the binding constraint on the loan size.)

(1) 67.5%
(2) 70%
(3) 72%
(4) 75%

Answer 19

2

super easy!
divide the mortgage 84,000 by the lending value 120,000

84,000/120,000
=70%

Question 20

Jason Buyer offers $345,000 to purchase a house, subject to obtaining an acceptable first mortgage. A lender has appraised the property at $340,000, requires an 80% loan to value ratio, and a 28% gross debt service ratio. Property taxes are $2,200 per annum and Mr. Buyer’s gross income is $75,000 per year.

What is the maximum amount (rounded to the nearest dollar) this lender will advance if the interest rate is j2 = 5%, the amortization period is 25 years, and payments are made monthly?

(1) $272,000
(2) $269,370
(3) $275,280
(4) $267,420

Answer 20

2

340,000 X .80
272,000.00

.28=pmt + 2,200
_____
75,000

21,000=pmt = tax
21,000-2,200/12= 1566.66

j2=5%
n=25(300)

? -1,566.66 0

=$269,370

Question 21

If Jeff applies for a mortgage loan with gross income of $3,000 per month, property taxes are estimated at
$200 per month, and the lender’s permitted gross debt service ratio is 30%, what can Jeff afford to pay for monthly principal and interest?

(1) $840
(2) $750
(3) $700
(4) $620

Answer 21

3

.30 = pmt + 200
_________
3,000

.30(3000) = 900
900-200
=700

Question 22

Given the following information, calculate the minimum annual income a buyer must have in order to qualify for a $42,500 loan.

Interest rate: 11 1/4% per annum, compounded semi-annually
Term: 5 years
Amortization period: 25 years
Payments: Monthly
Maximum Gross Debt Service Ratio: 27%
Property Taxes: $600 per annum

(1) $20,728.89
(2) $18,506.67
(3) $19,490.52
(4) $5,596.80

Answer 22

1

oh my freaking mother %^$# we finally figured this out.

ok first,

j2=11.25
n=25(300)
42,500 ? 0

=416.39
416.39 X 12 = 4996.80

THIS WAS THE TOUGH PART!!

THEN GO

.27(?) -600 = 4,996.80
.27(?) = 4996.80 + 600
.27(?) = 5,596.80
5,596.80/.27 = 20,728.88!!!!!!!!!!

Question 23

A potential borrower with an annual income of $58,000 and property taxes of $2,000 per annum has been told by a mortgage lender that the largest loan available will be $190,451. What is the maximum gross debt service ratio allowed by the lender given that the loan has monthly payments and is to be written at 5.5% per annum, compounded semi-annually and amortized over 25 years?

(1) 25%
(2) 27.5%
(3) 28.5%
(4) 30%

Answer 23

2

god this is tricky but i think we got it
so first find out what the monthly payment would be

j2= 5.5%
n=25
190,451 ? 0

=1,162.49
THEN WE NEED TO MULTIPLY THIS BY 12 TO GET THE ANNUAL PAYMENT

=13,949.880
then plug into the equation

gdsr? = 13,949.880 (anual payment) + 2000
_______________________
58,000

15949.88
_______
58,000

=.274998

Question 24

Given the following information, calculate the minimum annual income a buyer must have in order to qualify for a $150,000 loan.

Interest rate: 4.75% per annum, compounded semi-annually
Term: 5 years
Amortization period: 25 years
Payments: Monthly
Maximum Gross Debt Service Ratio: 32%
Property Taxes: $2,600 per annum

(1) $31,919.79
(2) $40,044.25
(3) $43,794.66
(4) $36,987.91

Answer 24

2
ok the biggest nightmare on these ones, you have to remember after you figure out the payment, you have to multiply it by 12 before putting it into the equation!!!!

so..

j2=4.75
n=25

150,000 ? 0

=851.18
THEN MULTIPLY BY 12!!!!!
=10,214.20

32% = PMT + 2,600
___________
income

32% = 10,214.20 +2,600

32%( ) = 12,814.20
12,814.20/32%
=40,044.25

Question 25

Allison Gunther, a prospective home buyer, has applied for a mortgage loan to finance the purchase of a townhouse for $175,000. Assume that the monthly payments on Ms. Gunther’s loan are agreed to be
$1,200 and property taxes are $1,500 per annum.

Calculate the minimum level of borrower’s annual income necessary to support these monthly payments based on the lender’s gross debt service ratio of 30%.

(1) $53,000
(2) $48,000
(3) $50,500
(4) insufficient information to calculate

Answer 25

1

think we getting better at these!!

soon as I saw the monthly payment of 1,200 multiply it by 12 and plug it into the equations

30% = 14,400 + 1500
___________
anual income
30%( ) = 15,900.00
15,900.00/30%
=53,000

Question 26

If an applicant for a mortgage loan has income of $1,000 per month and property taxes are estimated at $600 per year and the permitted gross debt service ratio is 30%, what can the applicant afford to pay for monthly principal and interest?

(1) $285
(2) $240
(3) $300
(4) $250

Answer 26

4

.30 = PMT + 50 (600 divided by 12)

.30 X 1000-50

=250

or

30% = _____ + 600
12,000

36,000= ____ + 600

3,000/12= 250

Question 27

A young executive has applied to her bank for a mortgage loan to enable her to purchase a house. Her income is $45,000 per year. The bank informs her they will apply a 30% gross debt service ratio when calculating her maximum loan, and that current mortgage rates are 6% per annum, compounded semi- annually for 20-year amortization mortgages. Given that annual property taxes are $1,500 and mortgage payments are to be made monthly, what is the maximum mortgage loan the bank will grant?

(1) $137,963.81
(2) $152,698.35
(3) $147,986.22
(4) $140,412.28

Answer 27

4

.30 = (pmt) + 1,500(tax)
____________
45,000

= 1000 per month

j2= 6%
n=20

? -1000 0

= 140,412.28

Question 28

A potential borrower with an annual income of $48,000 and property taxes of $2,000.16 per annum has been told by a mortgage lender that the largest loan available will be $177,667. What is the maximum gross debt service ratio allowed by the lender given that the loan has monthly payments and is to be written at 5% per annum, compounded semi-annually and amortized over 25 years?

(1) 25%
(2) 27.5%
(3) 32%
(4) 30%

Answer 28

4

ok thank god we got this one

j2 = 5%
n=25

177,667 ? 0
=1,033.32

REMEMBER TO MULTIPLY BY 12 TO GET THE PAYMENT
=12,399.84
THEN PLUG..

gdsr = pmt (12,399.84) + 2,000.16
_____________________
48,000

=30%

Question 29

Given the following information, calculate the minimum annual income a buyer must have in order to qualify for a $42,500 loan.

Interest rate: 11 3/4% per annum, compounded semi-annually Term: 5 years
Amortization period: 25 years Payments: Monthly
Maximum Gross Debt Service Ratio: 28% Property Taxes: $600 per annum

(1) $20,728.89
(2) $20,620.29
(3) $16,939.56
(4) $19,161.78

Answer 29

2

ok, we getting a hold on these ones now!

first find the payment

j2 = 11.75
n=300

42,500 ? 0

431.13
then multiply by 12 to get the annual payment (5173.65) and plug into the equation

.28(gdsr) = 5173 + 600
________
?

5773.00/.28=20,617

Question 30

A young executive has applied to her bank for a mortgage loan to enable her to purchase a house. Her income is $55,000 per year. The bank informs her that they will apply a 32% gross debt service ratio when calculating her maximum loan, and that current mortgage rates are 7% per annum, compounded semi- annually for 20-year amortization mortgages. Given that annual property taxes are $2,000 and mortgage payments are to be made monthly, what is the maximum mortgage loan the bank will grant?

(1) $168,982.46
(2) $183,932.97
(3) $163,246.79
(4) $200,937.47

Answer 30

1

.32= pmt + 2000
_________
55,000

j2 = 7%
n=20(240)

? 1,300.00 0

=168,982.46