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MA170wk10solns

# MA170wk10solns - MA170 Week 10 Report Amortized Loans...

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MA170 Week 10 Report: Amortized Loans Name: _________SOLUTIONS_______ Lab: Fall 2010 1. [9 marks ] Henry plans to purchase a car worth \$30 000 on January 1st of 2011 with a down payment worth 12% of the purchase price. The remaining cost will be covered by a loan with an interest rate of j 52 = 3% . The loan will be repaid with weekly payments over a °ve year period and the °rst payment is to be made one week after the purchase of the vehicle. (a) Determine the size of Henry’s weekly car payments. 30000 (0 : 88) = 26400 = Ra 52(5) e i ) R = 26400 1 ° ° 1 + 0 : 03 52 ± ° 52(5) 0 : 03 52 : = \$109 : 37 (b) Calculate Henry’s outstanding loan balance after two years using (i) the prospective method; Periods remaining: 5(52) ° 2(52) = 156 B 52(2) = Ra 5(52) ° 2(52) j = 109 : 37 0 B B B @ 1 ° ° 1 + 0 : 03 52 ± ° 156 0 : 03 52 1 C C C A : = 16311 : 97 (ii) the retrospective method. B 52(2) = A (1 + i ) 104 ° Rs 104 j i = 26400 ° 1 + 0 : 03 52 ± 52(2) ° 109 : 37 0 B B B @ ° 1 + 0 : 03 52 ± 52(2) ° 1 0 : 03 52 1 C C C A : = \$16312 : 84 (c) Which of the two methods used in (b) is more accurate, and why? The retrospective method is more accurate. Since the payments have been rounded, the °nal payment will be an irregular one. The prospective method assumes that the °nal payment is the same as all others, but the retrospective method uses the value of all payments already made, which will be the rounded value and the °nal payment is not needed for the calculation. 1

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2. [9 marks ] Five years ago a company borrowed \$100 000. The loan agreement stipulated that the loan would be amortized over a 10 year period and would be repaid with quarterly payments at j 2 = 6% : Recently, interest
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MA170wk10solns - MA170 Week 10 Report Amortized Loans...

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