chapter 10 amortization Flashcards
Which of the following statements regarding constant payment mortgages is TRUE?
- There are only three basic financial components in all constant payment mortgages: amortization period, nominal rate of interest, and the loan amount.
- Constant payment mortgages are repaid by equal and consecutive instalments that include principal and interest.
- If a mortgage payment frequency and interest rate compounding frequency are both monthly, an interest rate conversion is required for mortgage finance calculations.
- At the end of the amortization period, a constant payment mortgage’s future value is always equal to 10% of the loan’s face value.
Correct Answer: 2
Option (2) is correct because constant payment mortgages are repaid by equal periodic payments that occur in consecutive instalments including the principal amount and interest. Option (1) is incorrect because there are four basic financial components in all constant payment mortgages: loan amount, nominal rate of interest, amortization period, and payment. Option (3) is incorrect because when the mortgage payment frequency and interest rate compounding frequency are the same (monthly in this case), an interest rate conversion is NOT required for mortgage finance calculations. Option (4) is incorrect because at the end of the amortization period, a constant payment mortgage’s future value is equal to zero. This is because constant payment mortgages are always completely paid off at the end of the amortization period.
Which of the following statements regarding accelerating payments is TRUE?
- The accelerated biweekly payment method is typically most beneficial for mortgage loan borrowers who are paid monthly.
- Assuming that mortgage payments are constant, the more frequent mortgage payments are made, the longer the loan’s amortization period will become.
- Accelerating payments enable mortgage loan borrowers to pay off mortgage loans faster and reduce their interest costs.
- Accelerating payments will increase interest payments for mortgage loan borrowers.
Correct Answer: 3
Option (3) is correct because an accelerated payment means that mortgage loan borrowers can pay off more than the required minimum of each payment. This will decrease the interest paid over the loan term and the time needed to pay off the loan. Option (1) is incorrect because the accelerated biweekly payment method is typically most beneficial for mortgage loan borrowers who are paid biweekly, so that payments are made at the same frequency as income is received. Option (2) is incorrect because assuming that each mortgage payment is equal, the more frequent the payments are made, the shorter the loan’s amortization period becomes. This is because more of the principal is paid off faster, decreasing the time required to fully pay off the loan. Option (4) is incorrect because accelerating payments decreases the amount of time it takes to pay off the loan, which in turn decreases interest payments for mortgage loan borrowers.
Alex Ovichken is applying for mortgage financing in order to purchase a hockey rink. What is the maximum loan allowable (rounded to the nearest dollar), given payments of $4,000 per month, an interest rate of 5% per annum, compounded annually, and an amortization period of 20 years?
- $688,245
- $611,774
- $656,101
- $671,876
Correct Answer: 2
Option (2) is correct because the maximum allowable loan Alex could receive is $611,774, rounded. The interest rate must first be converted to an equivalent nominal rate with monthly compounding and the amortization period changed to months. Then solve for PV, the maximum loan allowable.
PRESS
DISPLAY
5 ⬛ NOM%
5
1 ⬛ P/YR
1
⬛ EFF%
5
12 ⬛ P/YR
12
⬛ NOM%
4.888949
4000 +/– PMT
–4,000
20 × 12 = N
240
0 FV
0
PV
611,773.770476
Mackenzie has purchased a new home and has arranged a mortgage loan with a face value of $700,000, an interest rate of j2 = 7.5%, an amortization period of 25 years, and a term of 3 years. Mackenzie is considering three repayment plans with different payment frequencies:
Option 1: Constant monthly payments
Option 2: Biweekly payments
Option 3: Accelerated biweekly payments
All options require the mortgage payments to be rounded up to the next highest dollar.
If Mackenzie chooses Option 1, calculate the amount of principal repaid over the term, interest paid during the term, and the outstanding balance owing at the end of the term, respectively, rounded to the nearest dollar.
$32,645; $151,711; $667,355
$35,677; $152,403; $669,323
$39,863; $149,187; $660,137
$50,109; $149,571; $649,891
Correct Answer: 1
Option (1) is correct $32,645 principal is paid off over the term, $151,711 interest is paid during the term, and the outstanding balance at the end of the term is $667,355.
PRESS
DISPLAY
7.5 ⬛ NOM%
7.5
2 ⬛ P/YR
2
⬛ EFF%
7.640625
12 ⬛ P/YR
12
⬛ NOM%
7.385429
700000 PV
700,000
25 × 12 = N
300
0 FV
0
PMT
–5,120.884417
5121 +/– PMT
–5,121
1 INPUT 36 ⬛ AMORT
PER 1 – 36
=
–32,645.08304
Principal repaid over term
=
–151,710.91696
Interest paid during term
=
667,354.91696
OSB36
Mackenzie has purchased a new home and has arranged a mortgage loan with a face value of $700,000, an interest rate of j2 = 7.5%, an amortization period of 25 years, and a term of 3 years. Mackenzie is considering three repayment plans with different payment frequencies:
Option 1: Constant monthly payments
Option 2: Biweekly payments
Option 3: Accelerated biweekly payments
All options require the mortgage payments to be rounded up to the next highest dollar.
If Mackenzie chooses Option 2, calculate the amount of principal repaid over the term, interest paid during the term, and the outstanding balance owing at the end of the term, respectively, rounded to the nearest dollar.
$34,645; $153,711; $662,355
$50,109; $149,571; $649,891
$32,677; $151,403; $667,323
$39,863; $149,187; $660,137
Correct Answer: 3
Option (3) is correct because $32,677 principal is paid off over the term, $151,403 interest is paid during the term, and the outstanding balance at the end of the term is $667,323.
PRESS
DISPLAY
7.5 ⬛ NOM%
7.5
2 ⬛ P/YR
2
⬛ EFF%
7.640625
26 ⬛ P/YR
26
⬛ NOM%
7.37323
700000 PV
700,000
25 × 26 = N
650
0 FV
0
PMT
–2,359.581163
2360 +/– PMT
–2,360
1 INPUT 78 ⬛ AMORT
PER 1 - 78
=
–32,676.947567
Principal repaid over term
=
–151,403.052433
Interest paid during term
=
667,323.052433
OSB78
Mackenzie has purchased a new home and has arranged a mortgage loan with a face value of $700,000, an interest rate of j2 = 7.5%, an amortization period of 25 years, and a term of 3 years. Mackenzie is considering three repayment plans with different payment frequencies:
Option 1: Constant monthly payments
Option 2: Biweekly payments
Option 3: Accelerated biweekly payments
All options require the mortgage payments to be rounded up to the next highest dollar.
If Mackenzie chooses Option 3, calculate the amount of principal repaid over the term, interest paid during the term, and the outstanding balance owing at the end of the term, respectively, rounded to the nearest dollar.
$45,863; $139,187; $660,137
$50,196; $149,562; $649,804
$42,645; $131,711; $637,355
$52,677; $159,403; $657,323
Option (2) is correct because $50,196 principal is paid off during the term, $149,562 interest is paid during the term, and the outstanding balance at the end of the term is $649,804.
PRESS
DISPLAY
7.5 ⬛ NOM%
7.5
2 ⬛ P/YR
2
⬛ EFF%
7.640625
12 ⬛ P/YR
12
⬛ NOM%
7.385429
700000 PV
700,000
25 × 12 = N
300
0 FV
0
PMT
–5,120.884417
÷ 2 =
–2,560.442209
2561 +/– PMT
–2,561
7.5 ⬛ NOM%
7.5
2 ⬛ P/YR
2
⬛ EFF
7.640625
26 ⬛ P/YR
26
⬛ NOM%
7.37323
N
526.94269
1 INPUT 78 ⬛ AMORT
PER 1 – 78
=
–50,196.476468
Principal repaid over term
=
–149,561.523532
Interest paid during term
=
649,803.523532
OSB78
Two years ago, Fraser and Glen purchased a car wash as an income-generating investment. They financed most of the purchase price with a $600,000 mortgage loan, written at an interest rate of 7.25% per annum, compounded annually. The loan has a 15-year amortization period, 5-year term, and calls for monthly payments rounded to the next higher dollar. Fraser and Glen know that interest paid on this mortgage is deductible from his income taxes. How much interest was paid during the third year of this mortgage? Round your final answer to the nearest dollar.
$39,676
$37,854
$31,495
$35,817
Correct Answer: 2
Option (2) is correct because interest paid during the third year is $37,854. To calculate the interest paid during the third year of this loan, the first step is to calculate the required monthly payments. Next, the total interest paid during the third year can be calculated based on the rounded payment.
PRESS
DISPLAY
7.25 ⬛ NOM%
7.25
1 ⬛ P/YR
1
⬛ EFF%
7.25
12 ⬛ P/YR
12
⬛ NOM%
7.019689
600000 PV
600,000
15 × 12 = N
180
0 FV
0
PMT
–5,399.576398
5400 +/– PMT
–5,400
25 INPUT 36 ⬛ AMORT
PER 25-36
= =
–37,854.050485
