Math Challenger Flashcards
What will be the purchase price of a mortgage which will provide the buyer with 48 payments of $650 plus an outstanding balance of $55,858.13 at the end of 48 months, if the buyer of the mortgage requires an effective annual yield of 15%?
(1) $55,698.26
(2) $54,867.08
(3) $52,536.87
(4) $58,989.30
1
j1=15%
n=48
? -650 55,858.13
=$55,698.25
A mortgage loan has a face value of $370,000, an interest rate of j2 = 5.5%, an amortization period of 20 years, a term of 3 years, and an option to make accelerated biweekly payments, rounded up to the next highest dollar. If this option is exercised, what is the outstanding balance owing at the end of the 3-year term?
(1) $232,928.17
(2) $311,500.07
(3) $328,192.44
(4) $317,935.02
3
i am close but..
j2 = 5.5% (convert to 26 payments) n= 20 X 13 =260
370,000 ? 0
then go input 36 amort
=329,930.34 which is very close!!!!
A local builder negotiates an interest only loan with ABC Finance Company. The face value of the loan is
$450,000, the interest rate is j2 = 8%, the term of the loan is 3 years, and the interest only payments are to be made monthly. What will be the size of the monthly interest only payments?
(1) $2,951.19
(2) $3,434.47
(3) $3,727.61
(4) $2,520.33
1
j2=8%
n=36
450,000 ? -450,000
=$-2,951.18
An investor wants to decide whether to buy a mortgage which calls for monthly payments of $390 for 20 years. If the investor can earn j2 = 8% in other investments, at what price should the mortgage be purchased?
(1) $48,921.57
(2) $46,626.12
(3) $45,232.84
(4) $47,081.12
4
2 2nd pmt 8 i/yr 2nd eff% 12 pmt 2nd i/yr =7.87 240 N -390 PMT = 226,037.44
then you are going to start from the very beginning again, and plug in the FV instead of the PMT to get the PV
2 2nd pmt 8 i/yr 2nd eff% 12 pmt 2nd i/yr =7.87 240 N FV = 226,037.44 PV = 47,081.12
Joanne Carmichael borrows $15,000 at a periodic interest rate of 0.5% per month. She agrees to repay $450 per month. For how many FULL years will Joanne have to make payments?
(1) 3
(2) 9
(3) 27
(4) 37
1
j1=6%
n=?
15,000 -450 0
=36.45 months(3)
A nominal interest rate of 8% per annum, compounded semi-annually is NOT equivalent to:
(1) an effective annual rate of 8.16%.
(2) 1.98039% per quarter.
(3) 4.85006% per annum, compounded monthly.
(4) 7.84499% per annum, compounded daily.
3
A private investor expects to receive $281.72 per month for a period of 17 years as a result of a mortgage loan she has just advanced. Calculate the investor’s expected yield (expressed as a nominal rate with semi- annual compounding) on her investment if the loan was for $23,250.
(1) 13.61433%
(2) 12.79841%
(3) 13.68893%
(4) 13.25002%
4
j12
n=17(204 months)
23,250 -281.72 0
=j12 converted to j2 = 13.250020
A mortgage loan has a face value of $350,000, an interest rate of j2 = 5.5%, an amortization period of 20 years, a term of 3 years, and an option to make accelerated biweekly payments. What is the amount of the accelerated bi-weekly payment rounded up to the next highest dollar?
(1) $1,325
(2) $2,533
(3) $1,198
(4) $2,649
3
j2=5.5
n=20
350,000 ? 0
=-2395.37
DIVIDED BY 2!! = 1,197.68
SO BASICALLY, WE DIVIDE THE PAYMENT BY WHATEVER THE ACCELERATION OPTION IS TO GET THE ANSWER!!!!
Steelgrave Developments is contemplating the construction of a large residential building. They have been guaranteed financing by their bank in the amount of $1,500,000. The terms of the financing are j2=9.75% with a 20-year amortization period, 5-year term, and monthly payments. Steelgrave believes that if market conditions are favourable, they will sell the building when it is completed, 2 years from now. How much principal will be paid off at the end of the 2-year construction period, rounded to the nearest dollar?
(1) $53,826
(2) $55,072
(3) $160,075
(4) $125,212
2
j2=9.75
n=20(240)
1,500,000 ? 0
=$55,071.67
A constant payment mortgage is written for $48,951.77 and specifies payments of $548.91 per month for 15 years. The interest rate on this mortgage is approximately:
(1) 12% per annum, compounded semi-annually.
(2) 8% per annum, compounded semi-annually.
(3) 10% per annum, compounded semi-annually.
(4) 11% per annum, compounded semi-annually.
4
j12=?
n=15(180)
48,951.77 -548.91 0
j12 conver to j2 = 11%
A private investor expects to receive $281.72 per month for a period of 17 years as a result of a mortgage loan he has just purchased for $21,000. Calculate the investor’s expected yield (expressed as a nominal rate with semi-annual compounding) on his investment.
(1) 14.997676%
(2) 15.233374%
(3) 14.971281%
(4) 15.613513%
2
j12 =?
n=17(204 months)
-21,000 281.72 0
convert j12 to j2 = 15.23
A mortgage loan has a face value of $300,000, an interest rate of j2 = 4%, an amortization period of 25 years, a term of 5 years, and an option to make accelerated biweekly payments, rounded up to the next highest dollar. If this option is exercised, what is the outstanding balance owing at the end of the 5-year term?
(1) $317,935.02
(2) $232,928.17
(3) $311,500.07
(4) $252,210.35
4
no freaking idea
im thinking its
j2=4 (convert to j26)
n= 25 X 13 months (1 extra because of 26 weeks
300,000 ? 0
65/input/shift/amort
A mortgage loan has a face value of $315,000, an interest rate of j2 = 4%, an amortization period of 20 years, a term of 5 years, and an option to make accelerated biweekly payments. What is the amount of the accelerated bi-weekly payment rounded up to the next highest dollar?
(1) $952
(2) $1,579
(3) $889
(4) $1,698
1
j2 = 4
n=20 (240)
315,000 ? 0
=1,903.37
divided by 2= 952 bi weekly payment
A borrower has arranged a $159,000 mortgage at j12=12% with a 20-year amortization, 5-year term and monthly payments. If all payments are paid when due, how much principal was paid off during the 5-year term?
(1) $289.11
(2) $13,541.84
(3) $145,873.23
(4) $13,126.77
4
j12 = 12%
n=20 (240)
159,000 ? 0
60/input/shift/amort
=$13,126.77
Fancy Finance Corporation has agreed to advance $370,000 to a real estate developer by way of an interest accruing loan. If Fancy Finance Corporation wants to earn an effective annual rate of 6% on the funds advanced, what is the amount they should receive from the developer in 30 days?
(1) $370,250.42
(2) $372,933.33
(3) $371,776.26
(4) Cannot be determined from the information given.
3
j1 = 6% (convert to j365) n= 365
370,000 ? -370,000
30/input/shift/amort
=1,772.10 + 370,000 = closest answer i could get
A mortgage loan with a face value of $150,000 is arranged through a mortgage broker. A commission of
$4,000, appraisal fees of $450, as well as survey and legal fees totalling $700 will be deducted from the face value before the funds are advanced to the borrower. Calculate the cost of funds advanced to the borrower, expressed as an effective annual interest rate (j1), if the loan is written at 6.75% per annum, compounded semi-annually, with monthly payments over a 20-year amortization period and a 5-year term?
(1) 7.803344%
(2) 7.537423%
(3) 9.581225%
(4) 8.540452%
1
KEY THING HERE, NOTICE THERE IS A 5 YEAR TERM!! THIS MEANS HAVE TO CALCULATE THE OSB60 second part
j2=6.75
n=20
150,000 ? 0
pmt=$1,132.26
j12=? (REMEMBER NEED TO CONVERT TO J1 AFTER)
n=60
144,850 -1,132.26 128,701.37 (OSB60!!!)
j12= 7.5 convered = 7.80
A mortgage for $200,000 is written at 6% per annum, compounded semi-annually. The mortgage calls for monthly payments rounded up to the next higher dollar, a 5-year term, and a 20-year amortization. The mortgage contract permits the borrower to prepay the full amount of the loan at any time subject to the payment of a three months’ interest penalty. At the time of prepayment, the current comparable interest rate is 4% per annum, compounded semi-annually.
If the borrower wishes to prepay this loan at the end of the first year (with the 12th payment), calculate the amount of the three months’ interest penalty.
(1) $969.01
(2) $15,504.15
(3) $5,687.99
(4) $2,883.28
4
ok, came up with yet another way that is even closer
go
j2=6%
n=20(240)
200,000 ? 0
=-1,424.37
then go 12/input/shift/amort
THEN!!! go show payments 13-15 which would be 3 payments and add the interest of the 3 of them 961 + 958 + 956 = 2,875 very close!!!
i think the thing on this one, is the comparable rate 4% might be to fool us.
j2 = 6%
n=20(240)
200 ? 0
=1424.37
j2=6% ( use instead of 4% gets alot closer)
n=60
200,000 -1424.37 169,592.08
osb 12 then add interest from months 13,14,15 gets really close!
A local mortgage broker has arranged a mortgage in the amount of $240,000. The borrower has agreed to pay a brokerage fee of $5,000 which is to be added to the loan amount, giving a face value of $245,000 for the loan.
The mortgage bears interest at a contract rate of 8% per annum, compounded quarterly. The mortgage has a term and amortization period of 25 years. The loan is to be repaid using monthly payments. The equivalent periodic interest rate, expressed as a rate per month on the funds advanced is:
(1) 0.682361%
(2) 0.821546%
(3) 0.752513%
(4) 0.514235%
1
A loan contract was written for a face value of $50,000 at j2 = 10.75% with a 20-year amortization and a 5-year term. Payments were to be made monthly in the amount of $499.76 and the outstanding balance at the end of the term was $45,167.50. A brokerage fee of $2,000 was deducted from the face value, so the funds actually advanced to the borrower were $48,000. What is the effective annual rate of interest on the funds advanced?
(1) 12.257094%
(2) 11.038905%
(3) 11.618034%
(4) 10.516863%
1
ok finally figured this out
READ CAREFULLY, IT WANTS YOU TO DETERMINE THE “ANNAUL RATE OF INTEREST”!!
j12 =?
n=60
48,000 -499.76 -45,167.50
then turn J12 into J1 (not J2)
J1 = 12.257094
Mary Smith has offered to purchase a house from a seller who is willing to provide partial financing. Her offer is a $75,000 down payment plus a mortgage of $125,000 at 4% per annum, compounded semi- annually. The loan is to be fully amortized with monthly payments of $755.31 over 20 years. If the market rate for similar mortgage loans is 7.5% per annum, compounded semi-annually, what is the market value of this offer, rounded to the nearest dollar?
(1) $169,579
(2) $108,618
(3) $94,579
(4) $183,618
1
j2 = 7.5
n=240
? -755.31 0
=94,579.01 + 75,000 down payment
= $169,579
A mortgage broker is arranging a partially amortized mortgage loan with a face value of $350,000. The loan contract is to be written at 6% per annum, compounded monthly. The repayment of the loan is to take place with monthly payments over an amortization period 15 years and a 5-year term. The borrower is to receive
$336,000 as a result of a broker’s commission of $10,000, a survey fee of $2,500, an appraisal fee of $500, and legal fees of $1,000, all of which are to be deducted from the face value. Calculate the cost of funds advanced to the borrower, expressed as an effective annual interest rate (j1).
(1) 7.296801%
(2) 9.942096%
(3) 8.407884%
(4) 7.163572%
1
NOTICE THERE IS A 5 YEAR TERM WHEN CACULATING THE COST OF FUNDS ADVANCED AS EFFECTIVE ANNUAL INTEREST RATE
j12=6%
n=15(180)
350,000 -2,953.49 0
j12=?
n=5(60 months)
336,000 -2,953.41 0sb60(266,031.76)
then convert j12 to j1 = 7.296
A borrower has proposals from four lenders to advance funds of $122,000 as a mortgage loan. Payments on each loan will be made annually.
A B C D Face Value 125,500 125,000 124,000 123,000 Amortization 8 yrs 5 yrs 7 yrs 6 yrs Rate: j2 = 6.6% 6.5% 6.75% 7%
Based on effective annual interest rates on funds actually advanced, which alternative should the borrower choose?
(1) A
(2) B
(3) C
(4) D
3
for each one what you have to do is
j2_6.6%
n=8
125,500 ? 0
then..
j1=?
n=8
122,000 -20,780.72 0
j1=7.4 actual interest rate
A mortgage for $300,000 is written at 6.5% per annum, compounded monthly. The mortgage calls for monthly payments rounded to the next higher dollar, a 5-year term, and a 25-year amortization. The mortgage contract permits the borrower to prepay the full amount of the loan at any time subject to the payment of an interest rate differential penalty. At the time of prepayment, the current comparable interest rate is 4.5% per annum, compounded monthly.
If the borrower wishes to prepay this loan at the end of the second year (with the 24th payment), calculate the amount of the interest rate differential penalty.
(1) $1,448.76
(2) $17,385.12
(3) $14,708.47
(4) $23,180.16
2
interest rate differential equation
mortgage balance X annual interest rate differntial (ie 6.5-4.5) X remaining terms in months
ok some progress here
so first…
j12 = 6.5
n=25(300)
? -2014.70 288,200.55
then..
288,200.55 X 2% (6.5% - 4.5% differencial)
=5,764.01
divided by 12 (monthly) = 480.33
480.33 X 36 osb24-02b60
=$17,292 super close!!
An offer of $235,000 is accepted, comprised of a cash down payment of $85,000 and a vendor-supplied mortgage loan of $150,000 at 5% per annum, compounded semi-annually. The loan has an amortization period of 25 years, a term of 5 years, and calls for monthly payments rounded up to the next higher dollar. Market rates of interest for equivalent mortgages are currently 8% per annum, compounded semi-annually.
The market value of the mortgage is:
(1) $132,849.12
(2) $199,309.00
(3) $235,000.00
(4) $217,849.12
1
ok so the confusion on this one, is we were adding 85,000 at the end, and when it says “what is the market value of the mortgage” i think that is different then when you add the 85,000. need to figure this out
j2 = 5%
n=25 (300)
150,000 ? 0
j2 = 8%
n=5(60)
? -862.82 (osb60) 132,216.34
=132,583.26
close!!
im guessing dont add the 85,0000 as well
