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1
Case Study
Students Name
Institutional Affiliation
Course Title
Professor’s Name
Date
2
Case Study
To analyze and advise Rebecca Young on Toronto apartment rental or purchase;
Calculation of Monthly Mortgage Payment:
Purchase Price = $700,000
Mortgage Rate = 7% APR
Mortgage Term = 10 years (converted to 20 semi-annual periods)
M=P
⋅
(1+r)n−1r(1+r)n
Where:
M = Monthly Mortgage Payment
P = Principal Loan Amount (80% of the purchase price)
r = Monthly Interest Rate (Annual Rate divided by 12)
n = Total Number of Payments (20 for a 10-year term)
Let's calculate the monthly mortgage payment:
Principal Loan Amount (P) = 80% of the purchase price = $700,000 * 0.80 = $560,000.
Monthly Interest Rate (r):
Annual Rate = 7%
Semi-annual compounding, so we need to calculate the semi-annual rate: 7% / 2 = 3.5%
per semi-annual period.
Monthly rate = (1 + 0.035)^(1/6) - 1 = 0.02798 (approximately).
Total Number of Payments (n) = 10 years * 2 (for semi-annual payments) = 20 payments.
3
Now, plug these values into the formula:
M = $560,000 \cdot \frac{0.02798(1 + 0.02798)^{20}}{(1 + 0.02798)^{20} - 1}
M ≈ $5,005.98 per month
So, Rebecca's monthly mortgage payment would be approximately $5,005.98.
Calculation of Principal Outstanding on Mortgage After 2 Years, 5 Years, and 10
Years:
We can use an amortization schedule to determine mortgage principle after 2, 5, and 10
years. Mortgage payments reduce principle.
Using the formula to calculate the principal outstanding at any point in time:
Pt=P(1−(1+r)−n)/r
Where:
P_t = Principal Outstanding after t periods (in our case, 2, 5, or 10 years)
P = Initial Principal Loan Amount ($560,000)
r = Monthly Interest Rate (0.02798)
n = Total Number of Payments (20)
Now, let's calculate the principal outstanding for each time period:
After 2 years:
P_2 = $560,000 * (1 - (1 + 0.02798)^(-2*20))/0.02798
P_2 ≈ $525,168.35
After 5 years:
P_5 = $560,000 * (1 - (1 + 0.02798)^(-5*20))/0.02798
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P_5 ≈ $479,930.63
After 10 years:
P_10 = $560,000 * (1 - (1 + 0.02798)^(-10*20))/0.02798
P_10 ≈ $381,367.36
So, the principal outstanding on the mortgage after 2 years is approximately $525,168.35,
after 5 years is approximately $479,930.63, and after 10 years is approximately
$381,367.36.
Calculation of Opportunity Costs:
Consider the alternative investment opportunity to assess the opportunity cost of
spending the required cash for closure (down payment and closing charges) instead of
leaving the money invested at the monthly rate. Rebecca's opportunity cost is the return
she could have made investing.
Rebecca said her investments earned the same effective monthly rate of return as her
mortgage. Since the mortgage monthly rate is 0.02798, we'll suppose her alternative
investment earns the same.
Let's compute monthly opportunity cost. Using the the formula for compound interest:
A=P(1+r)n
Where:
A = Future Value
P = Principal Amount (initial investment)
r = Monthly Interest Rate (0.02798)
5
n = Number of Months
For this estimate, Rebecca's down payment and closing fees are unknown, but let's
assume $200,000. She would have invested this money if not for the condo.
Now, let's calculate the opportunity cost for 2, 5, and 10 years:
After 2 years:
A_2 = $200,000 * (1 + 0.02798)^24
A_2 ≈ $232,081.14
After 5 years:
A_5 = $200,000 * (1 + 0.02798)^60
A_5 ≈ $268,884.23
After 10 years:
A_10 = $200,000 * (1 + 0.02798)^120
A_10 ≈ $343,469.47
Now that we have the future values of her investments after 2, 5, and 10 years, we can
calculate the opportunity cost by subtracting the initial investment from these values:
Opportunity Cost after 2 years: $232,081.14 - $200,000 = $32,081.14
Opportunity Cost after 5 years: $268,884.23 - $200,000 = $68,884.23
Opportunity Cost after 10 years: $343,469.47 - $200,000 = $143,469.47
Scenario Analysis:
6
Rebecca wants to know what would happen if she sold the condo in 2, 5, or 10 years
under four scenarios:
(a) Condo prices remain steady. (b) The condo price declines 10% over the next two
years, returns to its purchase price after five years, and rises 10% more by 10 years. (c)
Over 10 years, condo prices rise 2% annually due to inflation. (d) The condo price rises
5% annually for 10 years.
Let's analyze each scenario:
Scenario (a): Condo Price Remains Unchanged:
After 2 years:
Condo Price: $700,000
Principal Outstanding: $525,168.35
Realtor Fees (5%): $35,000
Other Closing Fees: $2,000
Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees
Net Gain/Loss = $700,000 - $525,168.35 - $35,000 - $2,000 = $137,831.65
After 5 years: Net Gain/Loss = $700,000 - $479,930.63 - $35,000 - $2,000 = $183,069.37
After 10 years: Net Gain/Loss = $700,000 - $381,367.36 - $35,000 - $2,000 =
$281,632.64
Scenario (b): Condo Price Drops 10% in 2 Years, Recovers, and Grows 10%:
After 2 years:
Condo Price: $700,000 - 10% = $630,000
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Principal Outstanding: $525,168.35
Realtor Fees (5%): $31,500
Other Closing Fees: $2,000
Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees
Net Gain/Loss = $630,000 - $525,168.35 - $31,500 - $2,000 = $71,331.65
After 5 years:
Condo Price: $700,000 Net Gain/Loss = $700,000 - $479,930.63 - $35,000 - $2,000 =
$183,069.37
After 10 years:
Condo Price: $700,000 + 10% = $770,000 Net Gain/Loss = $770,000 - $381,367.36 -
$38,500 - $2,000 = $348,132.64
Scenario (c): Condo Price Increases by 2% Annually:
In this scenario, the condo price increases by 2% per year. We'll calculate the future
condo price for each time period:
After 2 years: $700,000 * (1 + 0.02)^2 = $744,800
After 5 years: $700,000 * (1 + 0.02)^5 = $735,696
After 10 years: $700,000 * (1 + 0.02)^10 = $718,161.97
After 2 years:
Condo Price: $744,800
Principal Outstanding: $525,168.35
Realtor Fees (5%): $37,240
8
Other Closing Fees: $2,000
Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees
Net Gain/Loss = $744,800 - $525,168.35 - $37,240 - $2,000 = $180,391.65
After 5 years: Net Gain/Loss = $735,696 - $479,930.63 - $36,784.80 - $2,000 =
$216,880.57
After 10 years: Net Gain/Loss = $718,161.97 - $381,367.36 - $35,908.10 - $2,000 =
$298,886.51
Scenario (d): Condo Price Increases by 5% Annually:
In this scenario, the condo price increases by 5% per year. We'll calculate the future
condo price for each time period:
After 2 years: $700,000 * (1 + 0.05)^2 = $770,000
After 5 years: $700,000 * (1 + 0.05)^5 = $862,737.50
After 10 years: $700,000 * (1 + 0.05)^10 = $1,221,386.25
After 2 years:
Condo Price: $770,000
Principal Outstanding: $525,168.35
Realtor Fees (5%): $38,500
Other Closing Fees: $2,000
Net Gain/Loss = Condo Price - Principal Outstanding - Realtor Fees - Other Closing Fees
Net Gain/Loss = $770,000 - $525,168.35 - $38,500 - $2,000 = $204,331.65
9
After 5 years: Net Gain/Loss = $862,737.50 - $479,930.63 - $43,136.88 - $2,000 =
$337,669.99
After 10 years: Net Gain/Loss = $1,221,386.25 - $381,367.36 - $61,069.31 - $2,000 =
$776,949.58
Let's examine Rebecca's decision's quality. She wants to relocate to a house or penthouse
in 5–10 years. This means her apartment purchase should match her long-term aims and
lifestyle.
Qualitative Considerations:
Long-Term Goals:
Rebecca wants to move to a house or penthouse condo in five to ten years, so
buying an apartment may not be the best option. Condominium ownership may include
restrictions and prices that could prevent her from moving.
Flexible:
Renting lets Rebecca change her living arrangement as her work and life change.
For those with changing home demands, renting may be best.
Real estate market uncertainty:
The analysis scenarios show condo ownership benefits and losses. However, the
real estate market is uncertain, and many factors can affect prices. Rebecca must examine
her risk tolerance and market changes' influence on her finances.
Lifestyle:
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10
Rebecca should consider whether condo living fits her lifestyle. Condo upkeep
and association costs may effect her lifestyle and finances. Our recommendation for
Rebecca Young is based on financial analysis and qualitative factors.
Rebecca might rent a Toronto condo instead of buying. Her monthly mortgage
payments, property taxes, condo fees, and prospective maintenance charges could strain
her financially, especially considering her long-term aim of relocating to a house or
penthouse condo within five to 10 years. Renting allows her to adjust her living
environment as her profession and requirements change. Renting also decreases her real
estate market risk due to market uncertainties and price swings.
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I (1 Deintel
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$ 20,000.00
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What is the principal (loan)?
What is the payment per $1,000?
What is the monthly mortgage payment?
TABLE 15.1
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Term in Years
INTEREST
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5%
5½%
6%
6½%
7%
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8%
8½%
9%
9½%
10%
10½%
11%
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10.61
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11.36
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11.67
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8.72
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11.06
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6.52
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8.40
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6.60
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7.46
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8.06
8.37
8.68
9.00
9.33
9.66
9.99
10.33
22
5.44
6.20
6.51
6.82
7.13
7.44
7.75
8.07
8.39
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9.05
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Detemine the monthly principal and interest payment for a
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25
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4.0
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10.85263
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11.35480
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7.45573
6.75207
6.32068
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Exercise 10. Loan Payments A student loan of $50,000 at a fixed APR of 6% for
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РMТ
(-nY)1
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- Using this table as needed, calculate the required information for the mortgage. Amount Interest Financed Rate $88,500 8.00% Need Help? Read It Submit Answer Term of Loan (years) 30 Number of $1,000s Financed 88.5 Table Factor (in $) 7.34 Monthly Payment (in $) X LA Total Interest (in $) Xarrow_forwardMake an amortization table to show the first two payments for the mortgage. Amount of mortgage Annual interest rate Years in mortgage Monthly payment $407,181 5.50% 35 $2186.63 Question content area bottom Part 1 Month Monthly payment Interest Principal End-of-month principal 1 $2186.63 $enter your response here $enter your response here $enter your response here 2 $2186.63 $enter your response here $enter your response herearrow_forwardNeed Answer within given optionarrow_forward
- list K Complete the first month of the amortization schedule for a fixed-rate mortgage. Complete parts (a) through (d). Mortgage: $103,000 Interest rate: 5.5% Term of loan: 15 years Click the icon to view the Real Estate Amortization Table. Complete the first payment of the amortization schedule. (Do not round until the final answer. Then round to the nearest cent as needed.) Amortization Schedule Payment Number 1 Total Payment (a) $841.60 Interest Payment ... (b) $472.03 Principal Payment (c) $369.57 Balance of Principal Save (d) $472.03arrow_forwardDate Name Section 8.7 - Worksheet The Cost of Home Ownership Comparing Mortgage Interest for 30-year rate vs 15-year rate. In the lesson notes example, the $175,500 mortgage was financed with a 30-year fixed rate at 7.5%. The total interest paid over 30 years was approximately $266,220. a) Use the loan payment formula for installment loans to find the monthly payment if the time of the mortgage is reduced to 15 years. Round to the nearest dollar. b) Find the total interest paid over 15 years. c) How much interest is saved by reducing the mortgage from 30 to 15 years?arrow_forwardFor the second mortgage application, calculate the percentage of appraised value and the potential credit (in $). Appraised Lender's Value Percentage $125,500 60% Percentage of Appraised Value (in $) $ Balance of First Mortgage $53,200 $ Potential Credit (in $)arrow_forward
- Calculate the housing expense ratio and the total obligation ratio (in %) for the following mortgage applications. (Round your answers to two decimal places.) Monthly Other Monthly Housing Expense Ratio (%) Monthly Total Applicant Financial Obligations Ratio (%) Gross PITI Income Expense Obligations Martin $3,700 $605 $620 % Need Help? Read It I (1 Deintel DDECM ncO 14 IL015 MI ACK V oUD TO ACUED DDACTICE ANOTLUED DETALLC MY NOTESarrow_forwardPLEASE DO NOT ROUND THE ANSWERS Selling Price of Home Down Payment Rate of Interest Years $ 160,000.00 $ 20,000.00 3.50% 30 Required: Please use the above information to answer the below questions: (Use Table 15-1) How many total payments on this mortgage? What is the principal (loan)? What is the payment per $1,000? What is the monthly mortgage payment? TABLE 15.1 Amortization table (mortgage principal and interest per $1,000) Term in Years INTEREST 3½% 5% 5½% 6% 6½% 7% 7½% 8% 8½% 9% 9½% 10% 10½% 11% 10 9.89 10.61 10.86 11.11 11.36 11.62 11.88 12.14 12.40 12.67 12.94 13.22 13.50 13.78 12 8.52 9.25 9.51 9.76 10.02 10.29 10.56 10.83 11.11 11.39 11.67 11.96 12.25 12.54 15 7.15 7.91 8.18 8.44 8.72 8.99 9.28 9.56 9.85 10.15 10.45 10.75 11.06 11.37 17 6.52 7.29 7.56 7.84 8.12 8.40 8.69 8.99 9.29 9.59 9.90 10.22 10.54 10.86 20 5.80 6.60 6.88 7.17 7.46 7.76 8.06 8.37 8.68 9.00 9.33 9.66 9.99 10.33 22 5.44 6.20 6.51 6.82 7.13 7.44 7.75 8.07 8.39 8.72 9.05 9.39…arrow_forwardFinancial accounting question not used aiarrow_forward
- Part III: Loan comparison Consider the following loan information. term loan A 180 loan B 180 months amt $375,000 $375,000 rate 6.0% 7.0% points 3% 1% prepay 2% 1% 7. Calculate the loan payments and APR for each loan. 8 Create a spreadsheet & chart which compares the effective cost of borrowing (EBC) under Loan A vs. Loan B for each year of loan repayment.arrow_forwardquestion on the picarrow_forwarder A https://player-ui.mheducation.com/#/epub/sn_7cac#epubcfi(%2F6%2F326%5Bdata-uuid-ab153a0624d544c2822 6. Comparing Total Mortgage Payments. Which mortgage would result in higher total payments? Mortgage A: $970 a month for 30 years Mortgage B: $760 a month for 5 years and $1,005 for 25 years 1.1 20 far $120.000 storts ot 4.01arrow_forward
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