quiz 4-Part B - solution

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Langara College *

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4800

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Finance

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Apr 3, 2024

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Page 1 of 2 Quiz 4 Part B (solution) 1. (4 points) A company borrows $100,000 with interest at j 12 = 9%. The loan is to be amortized by monthly payments of $1550 for as long as necessary. A final smaller payment will be calculated so the loan will be exactly repaid. What is the amount of interest paid in the 2 nd monthly payment of $1550? I 1 = 100,000(0.0075) = 750; P 1 = 1550 - 750 = 800 OB 1 = 100,000 - 800 = 99,200; I 1 = 99,200(0.0075) = $744.00 2. (3 points) A company borrows $100,000 with interest at j 12 = 9% to be paid back by monthly payments. After 5 years, interest rates have dropped to j 12 = 6% and the company wishes to refinance their loan. The outstanding balance of the loan after 5 years (60 payments) is $39,660.90. If the company refinances the loan, they are subject to a penalty equal to 3 times one month's interest on the outstanding balance. Adding the penalty to the loan balance, and assuming the company will pay off the loan over 29 more months, what is the new monthly payment? Penalty = 39,660.90(0.0075) 3 = $892.37 New monthly payment = = $1505.71 3. (3 points) A loan of $10,000 is taken out and is to be paid back over 10 years using the sinking fund method. Annual interest payments on the loan are due at j 1 . Annual deposits into a sinking fund earning j 1 = 5% are made to accumulate the $10,000. The annual expense (cost) of debt is $1445. What is j 1 ? 1445 = 10,000( j 1 ) + = 10,000 j 1 + 795.05 which solves for j 1 = 6.50% 4. (4 points) A debt is amortized at j 4 = x % by payments of $300 per quarter. You are given that the outstanding balance is $6279.09 just after the k th payment and the outstanding balance is $6136.07 just after the ( k + 1) st payment. What is x ?
Page 2 of 2 B k = 6279.09, B k +1 = 6136.07 P k +1 = 143.02 I k +1 = 300 - 143.02 = 156.98 = B k i i = 156.98/6136.07 = 0.025 5. (3 points) A $100,000 debt is being repaid over 10 years using a sinking fund earning j 1 = 6%. What is the book value of the debt after 4 years? (Answer to the nearest dollar) Sinking fund deposit = = $7586.80 B 4 = 100,000 - 7586.80 = 100,000 - 33,189 = $66,811 6. (5 points) A city has two sources to borrow $200,000. The first source is to borrow at j 1 = 9% and amortize the debt for 10 years with annual payments of $31,164. For the second source, the money can be borrowed at j 1 = 8% if the interest is paid annually and the principal is repaid in a lump sum at the end of 10 years. Assume that a sinking fund can earn money at j 1 = x %. Find x where the second source will be cheaper? 31,164 = 200,000(0.08) + SF deposit; Thus SF deposit = 200,000/ = 15,164.00 Thus = 13.189; Therefore x = 6.013%. Any value of x greater than 6.013%.
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