wanted to own their home some day and have saved up $50,000. Talways tax of the
ID: 1175444 • Letter: W
Question
wanted to own their home some day and have saved up $50,000. Talways tax of the kind of homes they are interested in is about $3,000 are the recent mortgage rates for different terms quoted by the Royal Bank. 7. Robert and June Campbell have a combined income of $80,000, The The property O/year. Below Rate % (Semi-annual compounding) 7.00 7.50 8.00 8.25 8.50 Term 1 year 2 years 3 years 4 years 5 years (a) Using a GDS ratio of 30%, calculate the amount of first mortgage they can get under each term (five answers). (b) Now impose the 75%-appraised value rule. Can they get the loan in (a)?Explanation / Answer
The monthly mortgage payment formula is = Loan * [(r%) * (1+r%)t] / [ (1+r%)t - 1] ; where r% is the applicable monthly rate and t is the time period in months.
The GDS ratio = Monthly house related payment which is mortgage and taxes / monthly gross income
GDS ratio = (Monthly Mortgage Payment + 3000/12) / (80000/12) = 30%
Monthly Mortgage Payment = 1750
Now we plug the maximum monthly payment in the monthly payment formula and calculate the loan value for each of the 5 terms:
1 Year at 7% semi annual compounding. Effective annual rate = (1+7%/2)2 = 7.12% and this translates into monthly rate of (7.12%/12) = 0.59%
1750 = Loan * [(0.59%) * (1+0.59%)12] / [(1+0.59%)12 - 1] ; solving we get Loan = $20216.34
2 Year at 7.50% semi annual compounding. Effective annual rate = (1+7.5%/2)2 = 7.64% and this translates into monthly rate of (7.64%/12) = 0.64%
1750 = Loan * [(0.64%) * (1+0.64%)24] / [(1+0.64%)24 - 1] ; solving we get Loan = $38818.6
3 Year at 8% semi annual compounding. Effective annual rate = (1+8%/2)2 = 8.16% and this translates into monthly rate of (8.16%/12) = 0.68%
1750 = Loan * [(0.68%) * (1+0.68%)36] / [(1+0.68%)36 - 1] ; solving we get Loan = $55714.33
4 Year at 8.25% semi annual compounding. Effective annual rate = (1+8.25%/2)2 = 8.42% and this translates into monthly rate of (8.42%/12) = 0.70%
1750 = Loan * [(0.70%) * (1+0.70%)48] / [(1+0.70%)48 - 1] ; solving we get Loan = $71134.98
5 Year at 8.50% semi annual compounding. Effective annual rate = (1+8.50%/2)2 = 8.68% and this translates into monthly rate of (8.68%/12) = 0.72%
1750 = Loan * [(0.72%) * (1+0.72%)60] / [(1+0.72%)60 - 1] ; solving we get Loan = $85017.19
(b) Since the couple has saved $50000 for downpayment (seemingly) the 75% cap will not impact them in any term above.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.