Assignment-12

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New York Institute of Technology, Westbury *

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Finance

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Jan 9, 2024

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Real Estate Division
View Assignment Aman Preet Singh Student No: 4304704 Course: Real Estate Trading Services Licensing Course 2023 Assignment No: 12 You have submitted this assignment on 2023-10-08 . Green border - Questions answered correctly. Red border - Questions answered incorrectly. If you would like to print your assignment questions for future reference, you can do so by clicking the button below: Print this assignment THE NEXT FOUR (4) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Robert is selling his home to his good friend, Lisa. Robert is selling his waterfront multi-storey home for $3,950,000, and he will take back a mortgage for $2,000,000 at a contract rate of j = 4.5%, with a 25-year amortization period, a 3-year term, and monthly payments rounded up to the next higher $10. Question 1 Calculate the required monthly payment for this loan. $12,210 $9,240 $11,070 $10,270 Correct Answer: 3 Option (3) is correct because the required monthly payment is $11,070, rounded up to the next higher $10. PRESS DISPLAY 4.5 NOM% 4.5 2 P/YR 2 EFF% 4.550625 12 P/YR 12 NOM% 4.458383 2000000 PV 2,000,000 12 × 25 = N 300 0 FV 0 PMT –11,069.459086 Question 2 How much will Lisa owe Robert at the end of the 3-year term? $1,877,258.42 $1,586,475.64 $1,860,094.59 $1,203,363.14 2 Go to My Courses Page
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Correct Answer: 3 Option (3) is correct because $1,860,094.59 is owed at the end of the 3-year term. Continuing the calculations from the previous question, the outstanding balance at the end of the 36-month term is calculated as follows: PRESS DISPLAY 11070 +/– PMT –11,070 36 INPUT AMORT PER 36-36 = = = 1,860,094.58675 Question 3 Lisa is considering another possible mortgage, arranged through a mortgage broker. It will also have a face value of $2,000,000 with a contract rate of j = 5.5%, 25-year amortization period, 3-year term, and monthly payments rounded up to the next higher $10. However, the mortgage broker will take a brokerage fee of 3% of the loan's face value, which will be deducted from the face value of the loan. What effective annual interest rate will Lisa be paying on the funds advanced? 7.47287% 8.49535% 9.01523% 6.77619% Correct Answer: 4 Option (4) is correct because Lisa will pay an effective annual interest rate of 6.77619%. First, the face value of the loan is used to calculate the monthly payments. Then, the fees can be subtracted from the face value to calculate the rate paid on the funds advanced. The brokerage fee is $60,000 ($2,000,000 × 3%); therefore, the net amount advanced is $1,940,000 ($2,000,000 – $60,000). PRESS DISPLAY 5.5 NOM% 5.5 2 P/YR 2 EFF% 5.575625 12 P/YR 12 NOM% 5.438018 2000000 PV 2,000,000 12 × 25 = N 300 0 FV 0 PMT –12,207.829653 12210 +/– PMT –12,210 36 INPUT AMORT PER 36-36 = = = 1,877,258.41694 1877258.42 +/– FV –1,877,258.42 36 N 36 1940000 PV 1,940,000 I/YR 6.574422 EFF% 6.77619 Question 4 Assume that Lisa makes monthly payments of $12,000 and has an outstanding balance after 3 years (OSB ) of $1,885,450. If the market rate for similar mortgages is j = 6.5% and Lisa has made a down payment of $1,950,000, what is the market value of the offer? $1,141,387.31 $3,933,923.06 $2,742,373.06 $3,898,265.31 2 36 2
Correct Answer: 4 Option (4) is correct because the market value of the offer is $3,898,265.31. The payments of $12,000 and the outstanding balance of $1,885,450 can be discounted at the current rate of j = 6.5% to find the market value of the mortgage. The down payment is added to this number to determine the market value of the offer. PRESS DISPLAY 6.5 NOM% 6.5 2 P/YR 2 EFF% 6.605625 12 P/YR 12 NOM% 6.413688 12000 +/– PMT –12,000 1885450 +/– FV –1,885,450 36 N 36 PV 1,948,265.30965 + 1950000 = 3,898,265.30965 Question 5 Which one of the following statements regarding fees is TRUE? When a fee is deducted from a loan advance, it is referred to as a bonus. A lender bonus is a fee charged by lenders as a means of increasing their yield on a loan. When a fee is added to the face value of a loan, it is referred to as a discount. A brokerage fee is charged by borrowers to mortgage brokers for the brokerage's services in arranging a mortgage loan. Correct Answer: 2 Option (2) is correct because a lender bonus may be charged by lenders to borrowers as a means of increasing their yield on a loan. Option (1) is incorrect because when a fee is deducted from a loan advance, it is referred to as a discount. Option (3) is incorrect because when a fee is added to the face value of a loan, it is referred to as a bonus. Option (4) is incorrect because a brokerage fee is charged by mortgage brokers not borrowers for the mortgage broker's involvement in arranging a mortgage loan. Question 6 Robin owns a property that is subject to an existing mortgage. The $250,000 mortgage was obtained on January 1, 2020. The mortgage loan bears interest at a rate of 6.25% per annum, compounded semi-annually, and provides for monthly payments over a 20-year amortization period and a 10-year term. All payments have been made on time. On January 1, 2023, Robin wishes to prepay the remaining amount left on the mortgage, before the end of the loan's term. In order to do so, Robin will be subject to a penalty equal to three months' interest. What is the amount of the prepayment penalty that Robin will have to pay? $3,807.29 $3,077.25 $3,412.32 $3,533.77 2
Correct Answer: 4 Option (4) is correct because Robin's prepayment penalty is $3,533.77. First, determine the monthly payment and outstanding balance owing on the loan at the time of prepayment, i.e., at the end of 36 months. PRESS DISPLAY 6.25 NOM% 6.25 2 P/YR 2 EFF% 6.347656 12 P/YR 12 NOM% 6.17014 250000 PV 250,000 240 N 240 0 FV 0 PMT –1,815.702756 1815.7 +/– PMT –1,815.7 36 INPUT AMORT PER 36-36 = = = 229,088.703915 Then, calculate the penalty owing on the outstanding balance at the time prepayment is made Penalty = OSB × i × 3 The calculator steps continue as follows: PRESS DISPLAY RCL I/YR ÷ 12 = 0.514178 % 0.00514178 × 229088.7 = 1,177.924523 × 3 = 3,533.773568 Question 7 Which one of the following statements regarding portable mortgages is FALSE? The borrower can transfer the terms, conditions, and interest rate of the current mortgage to the home the borrower would like to purchase. If the current mortgage is too large for the new home, lenders will never allow the borrower to pay down a portion of the original balance without penalty. If the current mortgage is not large enough to cover the purchase of the new home, then the lender will often increase the mortgage and extend the borrower's loan term, providing the borrower's income and new property meet the lender's criteria. If the current posted rate for the new term is lower than the existing mortgage contract rate, the lender will typically blend the interest rates and the result will be a lower interest rate for the borrower. Correct Answer: 2 Option (2) is correct because if the current mortgage is too large for the new home, many institutions allow the borrower to pay down a portion (for example, 10%) of the original loan balance without penalty. If there was any remaining excess balance, it would be subject to a prepayment charge. Question 8 A property owner wants to sell a house and has it listed for $450,000. However, due to the dire condition of the real estate market, the property owner is having trouble selling that property. The owner decides to offer more advantageous financing options. Therefore, with a $400,000 mortgage, the market interest rate is j = 3.5% with monthly payments over a 20-year amortization period. However, the property owner (vendor) will accept lower payments of $1,800 per month instead of the contract payment. What is the market value of the mortgage, rounded to the nearest dollar? $310,366 $299,627 $242,373 $241,388 36 mo 12
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Correct Answer: 1 Option (1) is correct because the market value of the mortgage is $310,366. First, calculate the payment at the market rate and then determine the payment difference if the borrower makes payments of $1,800 per month. PRESS DISPLAY 400000 PV 400,000 3.5 I/YR 3.5 12 P/YR 12 20 × 12 = N 240 0 FV 0 PMT –2,319.838872 +/- –1800 –1,800 = 519.838872 The market payment is $2,319.84 per month. However, if the borrower only pays $1,800 per month, the financial benefit to the borrower is the payment difference of $519.84 per month ($2,319.84 – $1,800). To determine the market value of this arrangement, find the present value of the payment difference at the market rate over the amortization period. The calculator steps continue as follows: PRESS DISPLAY 519.84 +/- PMT –519.84 PV 89,633.811432 This present value represents the financial benefit the borrower would receive. Therefore, the market value of the mortgage equals the mortgage amount of $400,000 less the financial benefit of $89,634. The market value of the mortgage is $310,366 ($400,000 – $89,634). Question 9 According to the Business Practices and Consumer Protection Act (BPCPA), which of the following statements about annual percentage rate (APR) disclosure is TRUE? The BPCPA requires that mortgage brokers and lenders disclose the APR to individuals borrowing for family, household, or personal purposes. The only measure of the trust cost of the borrowing is the BPCPA's APR disclosure requirement. The BPCPA's APR is equal to the contractual interest rate plus interest finance charges. The BPCPA requires that certain mortgage contracts specify the interest rate as compounded annually or semi- annually. Correct Answer: 1 Option (1) is correct. The BPCPA requires that disclosure be given by mortgage brokers and lenders to individuals who borrow primarily for personal, family, or household purposes. Option (2) is incorrect because another measure of the true cost of borrowing is the cost of funds advanced to the borrower. Option (3) is incorrect because the BPCPA's APR is equal to the contractual interest rate plus non-interest finance charges. Option (4) is incorrect because the Interest Act requires that certain mortgage contracts specify the interest rate as compounded annually or semi-annually. Question 10 Which one of the following is NOT a potential advantage to a mortgage loan assumption? May allow the vendor to avoid prohibitive prepayment penalties if the alternative is to pay off the loan prior to maturity May facilitate a sale to a purchaser who cannot obtain conventional financing Helps reduce market interest rates by freeing up additional money for institutional lenders to lend out May help avoid fees, such as legal, appraisal, or insurance, that would be required in originating a new loan
Correct Answer: 3 Option (3) is correct because it is not a potential advantage that may arise as a result of a mortgage loan assumption because a mortgage assumption does not affect the amount of money that institutional lenders have available to lend out. In other words, there is no effect on the supply of money available for lending, which means there is no corresponding change to the market interest rate. THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A borrower must decide between the following two mortgage loans: Alternative A Alternative B Face Value $410,000 $405,000 Contract Rate (j ) 3.75% 3.5% Amortization Period 20 years 25 years Term 3 years 3 years Bonuses and Fees $7,500 $3,100 Net Proceeds $402,500 $401,900 Payments Monthly Monthly Question 11 Calculate the cost of funds advanced under Alternative A, expressed as an effective annual rate. Round your final answer to two decimal places. 3.75% 4.97% 4.50% 3.11% Correct Answer: 3 Option (3) is correct because the cost of funds advanced expressed as an effective annual rate is 4.50%, rounded. To calculate the cost of funds advanced, first calculate the payment and the outstanding balance. Then enter the net proceeds and change N to the length of the term. Solve for the j12 and j1 rates. PRESS DISPLAY 3.75 NOM% 3.75 2 P/YR 2 EFF% 3.785156 12 P/YR 12 NOM% 3.721034 20 × 12 = N 240 410000 PV 410,000 0 FV 0 PMT –2,424.666134 2424.67 +/– PMT –2,424.67 36 INPUT AMORT PER 36 36 = = = 366,146.304085 366146.3 +/– FV –366,146.3 36 N 36 402500 PV 402,500 I/YR 4.407303 EFF% 4.49743 2
Question 12 Calculate the cost of funds advanced under Alternative B, expressed as an effective annual rate. Round your final answer to two decimal places. 3.50% 4.46% 4.97% 3.82% Correct Answer: 4 Option (4) is correct because the cost of funds advanced expressed as an effective annual rate is 3.82%, rounded. To calculate the cost of funds advanced, first calculate the payment and the outstanding balance. Then enter the net proceeds and change N to the length of the term. Solve for the j and j rates. PRESS DISPLAY 3.5 NOM% 3.5 2 P/YR 2 EFF% 3.530625 12 P/YR 12 NOM% 3.474749 25 × 12 = N 300 405000 PV 405,000 0 FV 0 PMT –2,022.044846 2022.04 +/– PMT –2,022.04 36 INPUT AMORT PER 36 36 = = = 372,823.322649 372823.32 +/– FV –372,823.32 36 N 36 401900 PV 401,900 I/YR 3.75537 EFF% 3.820686 Question 13 The nuclear power plant has permanently shut down in Carlington, Ontario, and Marsha needs to sell her house to get a job in Toronto. However, she has had her house on the market for eight months now, and while there has been some interest, the deals always fall through due to loan qualification. With half of the town unemployed, it is difficult for many buyers to qualify for conventional financing. Marsha has had requests to offer vendor financing, but she turned them down because she considers them too risky. She is now reconsidering but wants to ensure she earns a rate of interest that will adequately compensate her for the risk she will be undertaking. She has received an offer to purchase for a $19,000 cash down payment plus vendor financing for $212,000. The partially amortized mortgage loan will have an interest rate of j = 6.25% (the market rate), a 25-year amortization, a 3-year term, and monthly payments. Marsha is considering a counter-offer with all the same terms, except increasing the interest rate to j = 11.75%. What is the market value of this counter offer? Hint: this is an example of vendor financing at an above-market interest rate, to reflect the higher risk involved in this situation. Round your final answer to the nearest dollar. $296,468 $328,468 $261,374 $239,863 12 1 2 2
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Correct Answer: 3 Option (3) is correct because the market value of offer is $261,374. First, calculate the monthly payments and the outstanding balance after the 36 payment, using the original interest rate of j = 11.75%. PRESS DISPLAY 11.75 NOM% 11.75 2 P/YR 2 EFF% 12.095156 12 P/YR 12 NOM% 11.472285 212000 PV 212,000 25 × 12 = N 300 0 FV 0 PMT –2150.619361 2150.62 +/– PMT –2150.62 36 INPUT AMORT PER 36-36 = = = 206,707.867448 Then calculate the market value of the mortgage using the market interest rate of j = 6.25%. The calculator steps continue as follows: PRESS DISPLAY 6.25 NOM% 6.25 2 P/YR 2 EFF% 6.347656 12 P/YR 12 NOM% 6.17014 206707.87 +/– FV –206,707.87 3 × 12 = N 36 PV 242,373.620595 The market value of the offer is: Market Value of Mortgage $242,374 + Cash Down Payment +19,000 Market Value of Offer $261,374 Question 14 Donald bought his house 3 years ago, at which time he arranged a $395,000 mortgage. This loan was written at a rate of 2.75% per annum, compounded semi-annually, with a 4-year term and 30-year amortization period. The loan has monthly payments of $1,610 and the outstanding balance due at the end of the 4-year term will be $359,032.96. Today, 36 months into this loan, Donald has received an offer from Tina to buy his house for $55,000 cash, plus assumption of the existing mortgage on the property. If current mortgage rates for 1-year terms are 4.25% per annum, compounded semi- annually, calculate the market value of Tina's offer, rounded to the nearest dollar. $418,133 $426,494 $398,125 $433,386 th 2 2
Correct Answer: 1 Option (1) is correct because the market value of offer is $418,133. The original monthly payments and outstanding balance after the 48 payment are given. As such, determine the market value of the assumed loan using the current mortgage interest rate of j = 4.25% for 1-year terms (the remaining time left in the term). PRESS DISPLAY 4.25 NOM% 4.25 2 P/YR 2 EFF% 4.295156 12 P/YR 12 NOM% 4.212851 1610 +/- PMT –1,610 359032.96 +/– FV –359,032.96 12 N 12 PV 363,133.266985 Cash Down Payment $55,000 + Market Value of Assumed Loan +363,133 Market Value of Offer $418,133 Question 15 A potential purchaser finds an attractive home listed for sale at $600,000 and submits an offer consisting of an $80,000 cash down payment subject to the vendor taking back a $520,000 mortgage at 3.99% per annum, compounded semi-annually. This loan will have a 20-year amortization, a 5-year term, and monthly payments. If 5-year term mortgages are currently being offered at 5.99% per annum, compounded semi-annually, calculate the market value of the offer, rounded to the nearest dollar. $574,038 $559,593 $651,897 $602,188 th 2
Correct Answer: 2 Option (2) is correct because the market value of the offer is $559,593, rounded. First, calculate the monthly payments and outstanding balance after the 60th payment, using the original interest rate of j2 = 3.99%. PRESS DISPLAY 3.99 NOM% 3.99 2 P/YR 2 EFF% 4.0298 12 P/YR 12 NOM% 3.957232 520000 PV 520,000 20 × 12 = N 240 0 FV 0 PMT –3,139.391387 3139.39 +/–PMT –3,139.39 60 INPUT AMORT PER 60-60 = = = 425,653.416791 Then calculate the market value of the mortgage using the market interest rate of j2 = 5.99%. The calculator steps continue as follows: PRESS DISPLAY 5.99 NOM% 5.99 2 P/YR 2 EFF% 6.0797 12 P/YR 12 NOM% 5.91659 425653.42 +/– FV –425,653.42 60 N 60 PV 479,592.848502 The market value of the offer is calculated as follows: Market Value of Mortgage $479,593 + Cash Down Payment + 80,000 Market Value of Offer $559,593 THE NEXT THREE (3) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Sunny wants to buy Gurjit's home in Victoria. Four years ago, Gurjit financed the $1,500,000 property with a cash down payment of $300,000 and private financing. The remaining portion of the purchase price was financed by Gurjit's friend, David, who lent the money to Gurjit at a rate of j = 6.25%, fully amortized over 25 years, with monthly payments of $7,856.90. Sunny is offering Gurjit a down payment of $250,000 and Sunny will assume the existing mortgage, which has 21 years remaining in the term. The current market rate of interest for similar mortgages is j = 7%. Question 16 What is the market value of Sunny's offer, rounded to the nearest dollar? $1,040,231 $1,294,238 $929,698 $1,035,889 2 2
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Correct Answer: 2 Option (2) is correct because the market value of Sunny's offer is $1,294,238, rounded to the nearest dollar. The market value of Sunny's offer is the sum of the $250,000 down payment and the present value of the promised payment stream. To find the present value of the payments, they must be discounted at the current rate of interest over the next 21 years. The current rate of interest must be converted to a monthly compounding rate. Then, using an N of 252 remaining payments, a monthly payment of $7,856.90, and a future value of 0, the present value of the payment stream can be calculated . PRESS DISPLAY 7 NOM% 7 2 P/YR 2 EFF% 7.1225 12 P/YR 12 NOM% 6.900047 7856.9 +/– PMT –7,856.9 21 × 12 = N 252 0 FV 0 PV 1,044,237.55324 + 250000 = 1,294,237.55324 Question 17 Assume instead that Gurjit's loan from David had a 5-year term with an outstanding balance of $1,081,798.70 owing at the end of the term (there is one year remaining in the term). The current market rate for 1-year term mortgages is 4.95% per annum, with semi-annual compounding. If all other factors remain as above, what is the market value of Sunny's offer, rounded to the nearest dollar? $1,514,521 $1,481,461 $1,264,521 $1,372,002 Correct Answer: 4 Option (4) is correct because the market value of Sunny's offer is $1,372,002, rounded to the nearest dollar. The solution is similar to the previous question except that you must use the outstanding balance at the end of the 5-year term as the future value when you are discounting with the market rate. Remember that, since the loan was initiated four years ago, there are only 12 payments (1 × 12) left in the 5-year term . PRESS DISPLAY 4.95 NOM% 4.95 2 P/YR 2 EFF% 5.011256 12 P/YR 12 NOM% 4.899712 7856.9 +/– PMT –7,856.9 1081798.7 +/– FV –1,081,798.7 12 N 12 PV 1,122,001.52238 + 250000 = 1,372,001.52238 The market value of Sunny's offer is $1,372,002, rounded to the nearest dollar. Question 18 If today's market interest rate for 1-year term mortgages was j = 4.55% and not j = 4.95%, the market value of Sunny's offer would: stay the same – the market interest rate does not affect the market value of the offer. decrease. increase. be impossible to determine without more information. 2 2
Correct Answer: 3 Option (3) is correct because as the market rate falls, the present value of payments received in the future increases, thus increasing the market value of the offer. Question 19 Increasing the size of the bonus on a bonused mortgage loan where the borrower pays the fee (while keeping the face value and all other loan terms constant) will cause the interest rate charged to the borrower on funds advanced to: increase. decrease. not change. change, but the direction of the change cannot be determined from the information given. Correct Answer: 1 Option (1) is correct because if the size of the bonus is increased, all other terms of the loan being kept constant, the effect will be that the borrower will be advanced less money, but will be making the same payments. Therefore, the borrower will be paying a higher interest rate on the funds advanced than when the bonus was smaller. Question 20 A mortgage broker has arranged a mortgage with a face value of $275,000. The mortgage has a contract rate of j = 4%, is fully amortized over 20 years, and is to be repaid with monthly payments. If the loan was sold to an investor immediately after it was initiated and the investor paid $260,000 for the loan contract, what rate of interest would be earned by the investor, expressed as an effective annual rate? Round your final answer to two decimal places. 5.01% 4.72% 5.67% 4.99% Correct Answer: 2 Option (2) is correct because the rate on funds advanced as an effective annual rate is 4.72%, rounded. This question requires calculation of the monthly rate of interest that will be earned by an investor who buys a series of payments. First, the monthly payment must be calculated. Then the amount the investor pays must be entered as a new present value. Finally, the rate of interest earned by the investor can be calculated, expressed as an effective annual rate. PRESS DISPLAY 4 NOM% 4 2 P/YR 2 EFF% 4.04 12 P/YR 12 NOM% 3.967068 20 × 12 = N 240 275000 PV 275,000 0 FV 0 PMT –1,661.677778 1661.68 +/– PMT –1,661.68 260000 PV 260,000 I/YR 4.619309 EFF% 4.718374 2