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Unformatted text preview: The Theory of Interest  Solutions Manual Chapter 8 1. Let X be the total cost. The equation of value is 12 where is the monthly rate of interest 10 j X X a j = && or 12 10. j a = && The unknown rate j can be found on a financial calculator as 3.503%. The effective rate of interest i is then ( 29 ( 29 12 12 1 1 1.03503 1 .512, or 51.2% i j = + = = . 2. Per dollar of loan we have 1 .12 18 1.12/18 L K n R = = = = and the equation of value 18 18 1.12 1 or 16.07143. 18 j j a a = = The unknown rate j can be found on a financial calculator as .01221. The APR is then ( 29 ( 29 APR 12 12 .01221 .1465, or 14.65%. j = = = 3. The equation of value is 16 16 7.66 100 or 13.05483. j a a = = The unknown rate j can be found on a financial calculator as .025. The APY is then ( 29 ( 29 12 12 APY 1 1 1.025 1 .3449, or 34.49%. j = + = = 4. ( a ) Amount of interest = Total payments − Loan amount Option A: ( 29 13 1000 12,000 1,000.00. = Option B: 12 .01 12,000 12 12,000 794.28. a ⋅ = Difference in the amount of interest = 1,000.00 − 794.28 = $205.72. ( b ) The equation of value is 12 12 12,000 1000 1000 or 11. j j a a = = Using a financial calculator .013647 j = and APR 12 .1638, j = = or 16.38%. 87 The Theory of Interest  Solutions Manual Chapter 8 ( c ) ( 29 APR 12 .01 12.00%, = = since the amortization rate directly gives the APR in the absence of any other fees or charges. 5. Bank 1: ( 29 ( 29 2 .065 .04708 . 24 L L X L + = = Bank 2: We have ( 29 1 12 1.126 1 .00994 j = = so that 24 .04704 . j L Y L a = = Bank 3: We have .01 j = and 24 .04707 . j L Z L a = = Therefore . Y Z X < < 6. ( a ) The United States Rule involves irregular compounding in this situation. We have ( 29 ( 29 [ ] ( 29 ( 29 [ ] ( 29 3 9 12 8000 2000 8000 .03 6240 6240 4000 6240 .06 2614.40 2614.40 1.03 $2692.83. B B X B = = = = = = = ( b ) The Merchant’s Rule involves simple interest throughout. We have ( 29 ( 29 ( 29 8000 1.12 2000 1.09 4000 1.03 $2660.00. X = = 7. ( a ) The interest due at time 1 t = is ( 29 10,000 .1 1000 = . Since only 500 is paid, the other 500 is capitalized. Thus, the amount needed to repay the loan at time 2 t = is ( 29 10,500 1.1 $11,550. = ( b ) Under the United States Rule, the interest is still owed, but is not capitalized. Thus, at time 2 t = the borrower owes 500 carryover from year 1, 1000 in interest in year 2, and the loan repayment of 10,000 for a total of $11,500. 8. ( a ) The equation of value is ( 29 ( 29 ( 29 ( 29 2 2 200 1 1000 1 1000 0 1 5 1 5 0. i i i i + + + = + + + = Now solving the quadratic we obtain ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 5 5 4 1 5 5 5 1 2 1 2 1.382 and 2.618 i ± ± + = = = so that .382 and 2.618 i = , or 38.2% and 261.8%....
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 Fall '09
 Depreciation, Annual Percentage Rate, Interest, Mortgage loan

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