assignment 10 Interest rates and Mortgages 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.
A borrower is considering mortgage loans from two different lenders. Lender A will loan funds at a rate of j2 = 8.5% and Lender B will loan funds at a rate of j12 = 8.6%. Which of the following represents the lowest cost of borrowing?
- j1 = 8.784900% with Lender B
- j1 = 8.839091% with Lender A
- j1 = 8.680625% with Lender A
- j1 = 8.947213% with Lender B
Correct Answer: 3
Option (3) is correct because Option (3) with Lender A has the lowest effective annual interest rate: (j1 = 8.680625%) and represents the lowest cost of borrowing. To compare rates, it is necessary to convert each rate into its equivalent effective annual rate and then compare from there.
PRESS
DISPLAY
Lender A
8.5 ⬛ NOM%
8.5
2 ⬛ P/YR
2
⬛ EFF%
8.680625
Lender B
8.6 ⬛ NOM%
8.6
12 ⬛ P/YR
12
⬛ EFF%
8.947213
Which of the following statements regarding interest rates is TRUE?
- Equivalent interest rates are different interest rates that result in different effective annual interest rates.
- Financial analysts prefer using effective rates because effective rates hide the impacts of compounding within the year.
- If two interest rates accumulate different amounts of interest for the same loan amount over the same time period, they have the same effective annual interest rate.
- Two interest rates are said to be equivalent if, for the same amount borrowed, over the same period of time, the same amount is owed at the end of the period of time.
Correct Answer: 4
Option (4) is correct because two interest rates are said to be equivalent if, for the same amount borrowed, over the same period of time, the same amount is owed at the end of the period of time. Option (1) is incorrect because equivalent interest rates are different interest rates that result in the same effective annual interest. Option (2) is incorrect because effective rates express the true rate of interest on an annual basis since the effective rate is the annual rate with annual compounding. Option (3) is incorrect because interest rates with the same effective annual interest rate accumulate the same amount of interest for the same loan amount over the same time 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.
Which of the following nominal and periodic interest rates is NOT equivalent to a periodic interest rate of iq = 2.22%?
j2 = 8.978568%
j12 = 8.815087%
imo = 0.765009%
iw = 0.169044%
Correct Answer: 3
Option (3) is correct because the monthly rate of 0.765009% is not equivalent. To compare the rates, it is necessary to convert the quarterly periodic rate of 2.22% to the corresponding nominal or periodic rates.
Option 1
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
2 ⬛ P/YR
2
⬛ NOM%
8.978568
Options 2 and 3
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
12 ⬛ P/YR
12
⬛ NOM%
8.815087 (j12)
÷ 12 =
0.734591 (imo)
Option 4
PRESS
DISPLAY
2.22 × 4 = ⬛ NOM%
8.88
4 ⬛ P/YR
4
⬛ EFF%
9.180105
52 ⬛ P/YR
52
⬛ NOM%
8.790288
÷ 52 =
0.169044
Alex and Kennedy are borrowing money to purchase a home and must choose between three mortgage options. The three different loans are identical except for the rate of interest charged. Assuming they prefer the lowest rate, which mortgage loan should they choose?
Loan A: 6.6% per annum, compounded quarterly
Loan B: 6.5% per annum, compounded annually
Loan C: 6.45% per annum, compounded daily
Loan A
Loan B
Loan C
They will be indifferent since the rates are all equivalent.
Correct Answer: 2
Option (2) is correct because Loan B has the lowest effective annual interest rate of j1 = 6.5%. To determine which loan the borrowers should choose, the effective annual rates need to be calculated for each loan.
PRESS
DISPLAY
LOAN A
6.6 ⬛ NOM%
6.6
4 ⬛ P/YR
4
⬛ EFF%
6.765154
LOAN B
6.5 ⬛ NOM%
6.5
1 ⬛ P/YR
1
⬛ EFF%
6.5
LOAN C
6.45 ⬛ NOM%
6.45
365 ⬛ P/YR
365
⬛ EFF%
6.66195
Compare the effective interest rates for loans A, B, and C and choose the lowest.
LOAN A: j1 = 6.765154%
LOAN B: j1 = 6.5%
LOAN C: j1 = 6.66195%
Harwinder and Suki have recently moved to Victoria because of job promotions. After renting for several months, they have bought a house just outside the city centre. Harwinder and Suki financed the purchase with a $425,000 mortgage at an interest rate of 4.99% per annum, compounded semi-annually, amortized over 25 years with a 5-year term and monthly payments.
What is the monthly payment?
- $2,469.40
- $2,790.49
- $2,151.49
- $2,520.43
Correct Answer: 1
Option (1) is correct because the monthly payment is $2,469.40. Payments are made monthly, so the given nominal rate with semi-annual compounding (j2 = 4.99%) must be converted to a j12 rate. Then the monthly payment can be calculated.
PRESS
DISPLAY
4.99 ⬛ NOM%
4.99
2 ⬛ P/YR
2
⬛ EFF%
5.05225
12 ⬛ P/YR
12
⬛ NOM%
4.938902
425000 PV
425,000
25 × 12 = N
300
0 FV
0
PMT
–2,469.402346
Harwinder and Suki have recently moved to Victoria because of job promotions. After renting for several months, they have bought a house just outside the city centre. Harwinder and Suki financed the purchase with a $425,000 mortgage at an interest rate of 4.99% per annum, compounded semi-annually, amortized over 25 years with a 5-year term and monthly payments.
If we now assume that the monthly payments are rounded up to the next higher dollar, calculate the outstanding balance at the end of the 5-year term, rounded to the nearest dollar.
- $355,261
- $376,057
- $384,245
- $368,053
Correct Answer: 2
Option (2) is correct because the outstanding balance at the end of the 60-month term is $376,057, rounded to the nearest dollar. First, round the payment found in the previous question up to the next higher dollar. Re-enter this new payment and then calculate the outstanding balance after 60 monthly payments. Continuing from the previous question, the calculator steps are as follows:
PRESS
DISPLAY
2470 +/– PMT
–2,470
60 INPUT ⬛ AMORT
PER 60-60
= = =
376,057.180051
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
A lender quotes a nominal interest rate of 6% per annum, compounded monthly (j12 = 6%). What is the equivalent nominal interest rate per annum, compounded quarterly?
6.16778%
6.34922%
6.64929%
6.03005%
Correct Answer: 4
Option (4) is correct because the equivalent rate is j4 = 6.03005%. This question requires an interest rate conversion from a j12 rate to its equivalent j4 rate.
PRESS
DISPLAY
6 ⬛ NOM%
6
12 ⬛ P/YR
12
⬛ EFF%
6.167781
4 ⬛ P/YR
4
⬛ NOM%
6.03005
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
Rank the following nominal and periodic rates from highest to lowest in terms of their effective annual rate:
id = 0.03%; j12 = 10.8%; iq = 2.7%; j52 = 10.5%; j2 = 10.4%
j2 = 10.4%; iq = 2.7%; id = 0.03%; j52 = 10.5%; j12 = 10.8%
j12 = 10.8%; j52 = 10.5%; id = 0.03%; iq = 2.7%; j2 = 10.4%
j12 = 10.8%; j52 = 10.5%; j2 = 10.4%; iq = 2.7%; id = 0.03%
Correct Answer: 1
Option (1) is correct because it gives the correct order of the nominal and periodic rates from highest to lowest in terms of their effective annual rate. To compare the various rates, they should all be converted into effective annual interest rates.
PRESS
DISPLAY
id = 0.03
.03 × 365 = ⬛ NOM%
10.95
365 ⬛ P/YR
365
⬛ EFF%
11.570175
iq = 2.7%
2.7 × 4 = ⬛ NOM%
10.8
4 ⬛ P/YR
4
⬛ EFF%
11.245326
j2 = 10.4%
10.4 ⬛ NOM%
10.4
2 ⬛ P/YR
2
⬛ EFF%
10.6704
j12 = 10.8%
10.8 ⬛ NOM%
10.8
12 ⬛ P/YR
12
⬛ EFF%
11.350967
j52 = 10.5%
10.5 ⬛ NOM%
10.5
52 ⬛ P/YR
52
⬛ EFF%
11.059303
