Assignment-10

pdf

School

New York Institute of Technology, Westbury *

*We aren’t endorsed by this school

Course

3211

Subject

Finance

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by DrTitanium9231

Real Estate Division

View Assignment Aman Preet Singh Student No: 4304704 Course: Real Estate Trading Services Licensing Course 2023 Assignment No: 10 You have submitted this assignment on 2023-09-27 . 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 Question 1 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. Question 2 A borrower is considering mortgage loans from two different lenders. Lender A will loan funds at a rate of j = 8.5% and Lender B will loan funds at a rate of j = 8.6%. Which of the following represents the lowest cost of borrowing? j = 8.784900% with Lender B j = 8.839091% with Lender A j = 8.680625% with Lender A j = 8.947213% with Lender B 2 12 1 1 1 1 Go to My Courses Page

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Correct Answer: 3 Option (3) is correct because Option (3) with Lender A has the lowest effective annual interest rate: (j = 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 THE NEXT FOUR (4) QUESTIONS REQUIRE YOU TO COMPLETE THE FOLLOWING TABLE: Loan Loan Amount Interest Rate (semi-annual compounding) Amortization Period (years) Monthly Payment A $180,000 j = 5.85% 25 years ? B $230,000 j = 6.5% ? $1,475.00 C ? j = 4.75% 20 years $822.00 D $350,000 ? 25 years $1,692.00 Question 3 Calculate the monthly payment for Loan A, rounded to the nearest cent. $1,093.79 $1,227.72 $1,135.65 $1,300.34 Correct Answer: 3 Option (3) is correct because the monthly payment is $1,135.65. Since the payments are monthly, the number of compounding periods (N) must also be in months. The given nominal rate with semi-annual compounding must first be converted to an equivalent nominal rate with monthly compounding. Then the payment can be calculated. PRESS DISPLAY 5.85 NOM% 5.85 2 P/YR 2 EFF% 5.935556 12 P/YR 12 NOM% 5.779952 180000 PV 180,000 12 × 25 = N 300 0 FV 0 PMT –1,135.65176 Question 4 Calculate the amortization period for Loan B. Between 20 and 25 years Between 25 and 30 years Between 30 and 35 years More than 35 years 1 2 2 2

Correct Answer: 2 Option (2) is correct because the amortization period is between 25 and 30 years (approximately 28 years). Since the payments are monthly, the given rate of j = 6.5% must first be converted to an equivalent j rate. Then, calculate the amortization period, expressed in months, and convert it into years. PRESS DISPLAY 6.5 NOM% 6.5 2 P/YR 2 EFF% 6.605625 12 P/YR 12 NOM% 6.413688 230000 PV 230,000 1475 +/– PMT –1,475 0 FV 0 N 336.227297 ÷ 12 = 28.018941 Question 5 Calculate the loan amount for Loan C, rounded to the nearest dollar. $127,700 $144,857 $132,211 $155,680 Correct Answer: 1 Option (1) is correct because the loan amount is $127,700, rounded. The given rate of j = 4.75% must first be converted to a j rate as the loan calls for monthly payments. Then the loan amount can be calculated. PRESS DISPLAY 4.75 NOM% 4.75 2 P/YR 2 EFF% 4.806406 12 P/YR 12 NOM% 4.703666 20 × 12 = N 240 822 +/– PMT –822 0 FV 0 PV 127,700.061259 Question 6 Calculate the nominal rate per annum, with semi-annual compounding, for Loan D. 2.698064% 3.197331% 4.229764% 5.562796% 2 12 2 12

Correct Answer: 2 Option (2) is correct because the nominal rate per annum, compounded semi-annually is j = 3.197331%. Since the loan calls for monthly payments, the number of compounding periods must be in months and the calculated interest rate must be compounded monthly. This j rate is then converted to a nominal rate with semi-annual compounding (j ). PRESS DISPLAY 350000 PV 350,000 25 × 12 = N 300 1692 +/– PMT –1,692 0 FV 0 12 P/YR 12 I/YR 3.176239 (j ) EFF% 3.222889 (j ) 2 P/YR 2 NOM% 3.197331 (j ) Question 7 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. Question 8 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. 2 12 2 12 1 2

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 9 Which of the following nominal and periodic interest rates is NOT equivalent to a periodic interest rate of i = 2.22%? j = 8.978568% j = 8.815087% i = 0.765009% i = 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 (j ) ÷ 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 Question 10 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: 7% per annum, compounded daily Loan B: 6.5% per annum, compounded monthly Loan C: 7% per annum, compounded quarterly Loan A Loan B Loan C They will be indifferent since the rates are all equivalent. q 2 12 mo w 12

Correct Answer: 2 Option (2) is correct because Loan B has the lowest effective annual interest rate of j = 6.697185%. To determine which loan the borrowers should choose, the effective annual rates need to be calculated for each loan. PRESS DISPLAY LOAN A 7 NOM% 7 365 P/YR 365 EFF% 7.250098 LOAN B 6.5 NOM% 6.5 12 P/YR 12 EFF% 6.697185 LOAN C 7 NOM% 7 4 P/YR 4 EFF% 7.185903 Compare the effective interest rates for loans A, B, and C and choose the lowest. LOAN A: j = 7.250098% LOAN B: j = 6.697185% LOAN C: j = 7.185903% THE NEXT TWO (2) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: 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 2.99% per annum, compounded semi-annually, amortized over 25 years with a 5-year term and monthly payments. Question 11 What is the monthly payment? $2,009.11 $2,358.59 $2,151.49 $2,520.43 Correct Answer: 1 Option (1) is correct because the monthly payment is $2,009.11. Payments are made monthly, so the given nominal rate with semi-annual compounding (j = 2.99%) must be converted to a j rate. Then the monthly payment can be calculated. PRESS DISPLAY 2.99 NOM% 2.99 2 P/YR 2 EFF% 3.01235 12 P/YR 12 NOM% 2.971543 425000 PV 425,000 25 × 12 = N 300 0 FV 0 PMT –2,009.1133 1 1 1 1 2 12

Question 12 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. $377,290 $363,140 $384,245 $398,053 Correct Answer: 2 Option (2) is correct because the outstanding balance at the end of the 60-month term is $363,140, 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 2010 +/– PMT –2,010 60 INPUT AMORT PER 60-60 = = = 363,139.97416 Question 13 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 $4,500 per month, an interest rate of 5% per annum, compounded annually, and an amortization period of 20 years? $611,774 $688,245 $656,101 $671,876 Correct Answer: 2 Option (2) is correct because the maximum allowable loan Alex could receive is $688,245, 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 4500 +/– PMT –4,500 20 × 12 = N 240 0 FV 0 PV 688,245.491785 Question 14 A lender quotes a nominal interest rate of 7.5% per annum, compounded monthly (j = 7.5%). What is the equivalent nominal interest rate per annum, compounded quarterly? 7.430976% 7.618169% 7.636791% 7.546973% 12

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Correct Answer: 4 Option (4) is correct because the equivalent rate is j = 7.546973%. This question requires an interest rate conversion from a j rate to its equivalent j rate. PRESS DISPLAY 7.5 NOM% 7.5 12 P/YR 12 EFF% 7.76326 4 P/YR 4 NOM% 7.546973 THE NEXT THREE (3) QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Mackenzie has purchased a new home and has arranged a mortgage loan with a face value of $700,000, an interest rate of j = 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. Question 15 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 OSB 4 12 4 2 36

Question 16 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 OSB Question 17 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 78

Correct Answer: 2 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 Question 18 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? $39,675.57 $37,854.05 $31,494.57 $35,817.23 Correct Answer: 2 Option (2) is correct because interest paid during the third year is $37,854.05. 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

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 19 Rank the following nominal and periodic rates from highest to lowest in terms of their effective annual rate: i = 0.03%; j = 10.8%; i = 2.7%; j = 10.5%; j = 10.4% j = 10.4%; i = 2.7%; i = 0.03%; j = 10.5%; j = 10.8% j = 10.8%; j = 10.5%; i = 0.03%; i = 2.7%; j = 10.4% j = 10.8%; j = 10.5%; j = 10.4%; i = 2.7%; i = 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 i = 0.03 .03 × 365 = NOM% 10.95 365 P/YR 365 EFF% 11.570175 i = 2.7% 2.7 × 4 = NOM% 10.8 4 P/YR 4 EFF% 11.245326 j = 10.4% 10.4 NOM% 10.4 2 P/YR 2 EFF% 10.6704 j = 10.8% 10.8 NOM% 10.8 12 P/YR 12 EFF% 11.350967 j = 10.5% 10.5 NOM% 10.5 52 P/YR 52 EFF% 11.059303 Question 20 The following information describes a residential mortgage loan: Loan Amount: $250,000 Interest Rate: j = 3.75% Fully amortized over 25 years with monthly payments Calculate the monthly payment and the interest portion of the second monthly payment. $1,281.39 and $773.65, respectively $1,232.85 and $741.14, respectively $1,399.52 and $866.67, respectively $1,138.63 and $922.26, respectively d 12 q 52 2 2 q d 52 12 12 52 d q 2 12 52 2 q d d q 2 12 52 2

Correct Answer: 1 Option (1) is correct because the monthly payment and the interest portion of the second monthly payment are $1,281.39 and $773.65, respectively. To answer this question, the first step is to determine the monthly compounded interest rate and the payment. Then the interest portion of the second payment can be computed. PRESS DISPLAY 3.75 NOM% 3.75 2 P/YR 2 EFF% 3.785156 12 P/YR 12 NOM% 3.721034 250000 PV 250,000 25 × 12 = N 300 0 FV 0 PMT –1,281.38997 1281.39 +/– PMT –1,281.39 2 INPUT AMORT PER 2-2 = = –773.645928