Math (Amortization) Flashcards
A borrower has arranged a $159,900 mortgage at j12=12% with a 25-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) $89,583.15
(2) $6,950.91
(3) $152,949.09
(4) $6,529.15
2
j12=12%
n=25(300)
159,000 ? 0
60/input/shift/amort = $6,950.91
Josie Purchaser arranged a mortgage loan for $75,000 at 9.5% per annum, compounded semi-annually, with a 25-year amortization period and monthly payments. What is her interest cost for the first month?
(1) $645.78
(2) $582.33
(3) $612.27
(4) $63.45
2
j2 = 9.5
n=25(300)
75,000 ? 0
1 input/shift/amort
=$582.33
A mortgage was written for $48,000 at an interest rate of j2 = 8%, an amortization period of 15 years, and monthly payments. Calculate the balance owing at the end of five years, rounded to the nearest dollar.
(1) $38,507
(2) $37,725
(3) $47,289
(4) $46,181
2
j2=8%
n=15(180)
48,000 ? 0
60/input/shift/amort
=$37,725
A borrower has arranged a loan of $32,000 at an interest rate of 7% per annum, compounded semi-annually with payments set at $1,400 per month. What is the amortization period of the loan?
(1) 23.603054 years
(2) 24.275695 years
(3) approximately 2 years
(4) approximately 20 years
3
j2 = 7%
n=?
32,000 -1,400 0
N=24.57 (2 years approximately)
A borrower has arranged a $159,000 mortgage at j2=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) $89,583.16
(2) $13,541.84
(3) $145,458.16
(4) $296.36
2
j2 = 12%
n=20(240)
159,000 ? 0
pmt = 1,718.75
60 input/shift/amort
= $-13,541
An agreement for sale in the amount of $150,000 requires the buyer to make payments of $1,250 per month for as long as necessary to fully amortize the loan at 8% per annum, compounded semi-annually. How many FULL payments of $1,250 will be required?
(1) 236
(2) 237
(3) 242
(4) 243
1
j2+8%
n=?
150,000 -1250 0
=236.56
A borrower has arranged a loan of $196,000 at an interest rate of 6% per annum, compounded annually over an amortization period of 15 years. What is the monthly payment required?
(1) $1,386.30
(2) $1,543.86
(3) $1,262.84
(4) $1,637.18
4
j1=6%
n=15 (180)
196,000 ? 0
convert j1 to j12
What is the amortization period of a $125,000 loan that has a term of 7 years, an interest rate of 6.5% per annum, compounded semi-annually, and monthly payments of $926.
(1) 300 months
(2) 250 months
(3) 239.803291 months
(4) impossible to determine from the information provided
3
j2= 6.5
n=?
125,000 -926 0
=239.80 months
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 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
Bona Fide Brokerage Ltd. arranges a mortgage with a face value of $55,000 for Gina Griffiths. Gina is obliged to make monthly payments at j2 = 12% for 15 years in order to fully amortize the loan. The broker deducts legal costs of $450 and a brokerage fee of $1,500 from the face value of the mortgage. Calculate the monthly payment.
(1) $649.89
(2) $567.55
(3) $632.17
(4) $626.85
1
j2 = 12%
n=15(180)
55,000 ? 0
=-649.89
A mortgage broker will advance $97,000 to a borrower who has agreed to pay a bonus of $2,200. As a consequence, the face value of the loan will be $99,200. The loan will be amortized over 25 years with monthly payments at j2 = 6%. Calculate the monthly payment required to amortize the loan.
(1) $620.62
(2) $634.69
(3) $690.83
(4) $650.74
2
ok, based on this, i am convinced we are supposed to use the face value all the time when calculating, unless they ask for the cost expressed as an interest rate??
j2=6%
n=25(300)
99,200 ? 0
=$634.68
An investor has decided to establish a bank account in order to accumulate sufficient capital at the end of seven years to purchase a boat. If the account pays interest at 3% per annum, compounded annually and the investor makes deposits of $8,000 at the end of each year, how much capital will he have accumulated at the end of seven years?
(1) $42,851.59
(2) $79,747.81
(3) $57,987.33
(4) $61,299.70
4
j1=3%
n=7
0 -8000 ?
=61,299.69
A holding property was purchased ten years ago for $23,000. How much must it sell for now if the owner is to realize a pre-tax yield of j2 = 14%?
(1) $85,266.09
(2) $89,002.74
(3) $92,516.82
(4) $83,144.22
2
j2 = 14%
n= 10
-23,000 0 ?
=89,002.74
Kevin wants to purchase an investment which will give him payments of $450 at the end of every quarter for the next four years. If Kevin wants to earn an interest rate of 6% per annum, compounded quarterly, how much should he pay today for this investment?
(1) $8,069.57
(2) $7,224.92
(3) $6,359.07
(4) $6,983.29
3
j4 = 6%
n=16
? 450 0
=-6359.06
What rate of interest per compounding period would allow savers to “double their money” in 8 compounding periods? Assume that you invest $100 today so that it will grow to $200 in eight compounding periods.
(1) 12.5%
(2) 10.609279%
(3) 25%
(4) 9.050773%
4
j1 = ?
n= 8
-100 0 200
=9.051
An investor has decided to establish a bank account in order to accumulate sufficient capital at the end of four years to purchase a boat. If the account pays interest at 2.5% per annum, compounded annually and the investor makes deposits of $6,000 at the end of each year, how much capital will she have accumulated at the end of four years?
(1) $24,915.09
(2) $26,491.51
(3) $28,018.91
(4) $25,357.92
1
j1=2.5
n=4
0 -6000 ?
=$24,915.09
A holding property was purchased 10 years ago for $23,000. How much must it sell for now if the owner is to realize a pre-tax yield of j2 = 6%?
(1) $30,910.08
(2) $41,540.56
(3) $45,189.50
(4) $38,246.54
2
j2=6%
n=10
-23,000 0 ?
=$41,540.55
Johnny F. Lane wants to purchase a sports car which will be introduced to the market 10 months from now for $19,800. How much money should Johnny deposit in the bank today if he can earn 9% per annum, compounded monthly in his savings account?
(1) $18,374.46
(2) $7,856.84
(3) $19,800.00
(4) $18,018.00
1
j12=9%
n=10
? 0 19,800
=-18,374.46
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 constant payment mortgage is written for $48,951.77 and specifies payments of $520 per month for 15 years. The interest rate on this mortgage is:
(1) j2 = 10.257982%
(2) j4 = 11.963722%
(3) j12 = 9.797818%
(4) all of the above
3
j12
n=15X12(180)
48,951.77 -520 0
j12=9.79
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
