# hw11-3 - \$5,000,000 the loan will never get paid off...

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Math 1160 - Section 11.3 Answer Key 1. Montonic – a, b, d, f, h 2. Increasing – a, b, d 3. Unbounded – b, d, e, f 4. Constant - g 5. Repelled from y = b/(1-a) – b, d, e, f 6. Decreasing – f, h 7. Absolute value of a < 1 – a, c, h 8. a < 0 – c, e 10. 12. 14. 16. 18. 20. 22. a = .98 (monotonic, attracted to y = 0) y 0 = 10 (initial value) 26. Solve b/(1-a) to get the maximum loan amount. The graph of a loan is monotonic (decreasing balance over time) and is repelled from the line (loan amount maximum). Difference equation y n = 1.02y n-1 – 100,000 a = 1.02 and b = -100,000 So b/(a-1) = -100,000/(1 – 1.02) = -100,000/-.02 = 5,000,000 **The loan amount must be less than \$5,000,000. If the loan amount if equal or greater than

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Unformatted text preview: \$5,000,000, the loan will never get paid off because the interest due each compounding period will exceed the loan payment made. 29. The difference equation for this loan is: y n = 1.05y n-1 – 1500 The graph of these values is monotonic ( a is positive) and repelled (absolute value of a is greater than 1). Therefore, the maximum that can be borrowed must be less than b /1-a so that the loan is eventually paid off. b /1-a = –1500/(1 – 1.05) = -1500/-.05 = 30,000 She must borrow less than = \$30,000. 30. Difference Equation y n = 1.01y n-1 – 120 y = 10,000 y = 10,000 y 1 = 1.01(10,000) – 120 = \$9,980 (\$20 applied to principal, \$100 applied to interest) y 2 = 1.01(9,980) – 120 = \$9,959.80 (\$20.20 applied to principal, \$99.80 applied to interest) *The difference in the loan balance from period to period shows how much of the \$120 payment was applied to the principal for that period. The remainder (\$120 payment – amount applied to principal) is for the interest (which is 1% of the beginning balance for that period)....
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hw11-3 - \$5,000,000 the loan will never get paid off...

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