MATH 320 Practice Test 3 - .~-~ II-ll PRACTICE MULTIPLE...

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---- .~._-----~----------_ .. -, II-ll PRACTICE MULTIPLE CHOICE TEST 3 1. A loan of 1000 is made at an interest rate of 12% compounded quarterly. The loan is to be repaid with three payments: 400 at the end of the first year, 800 at the end of the fifth year, and the balance at the end of the tenth year. Calculate the amount of the final payment. (A) 587 ~) 658 /- (C) 737 (D) 777 (E) 812 (E) 1073 (D) 1071 (B) 1067 (A) 1065 2. On January 1, 1996, Sam invests 1000 in a fund for which the force of interest at time t is expressed by .10(t - 1)2, where t is the number of years since January 1,1996. Calculate the accumulated value of the fund on January 1, 1998. / (f:) 1069 3. You are given Ot = 10~ t ' t 2:: O. Calculate a4j' 4. A car dealer offers to sell a car for 10,000. The current market loan rate is a nominal rate of interest of 12% per annum, compounded monthly. As an inducement, the dealer offers 100% financing at an effective annual interest rate of 5%. The loan is to be repaid in equal installments at the end of each month over a four-year period. Calculate the cost to the dealer of this inducement. 5. A 30-year bond has an annual coupon rate of 6% for the first 10 years, 7% for the next 10 years, 8% for the last 10 years, and matures at its par value of-lOO. The bond is bought to produce an effective annual yield rate of 7%. Determine an expression for the price of the bond. (All interest functions are at 7%.) ~J 100 - v2°aiOi + aiOi (oE) 100 + v20 aiOi - aiOi /
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- -~ ;6. Determine the present value of 1 payable at the end of years 7, 11, IS, 19,23, and 27. f. J'( a28i - a4j sJi + d CC) r",{1 ,--- a28i - a4j sJi + an (B) a28i - a4i sJi - an (D) (A) 7. You are given the following information: ! i , •• Qa QI QJ. ill •• (E) 5-: (E) 5Q - 4P z+2 Calendar Year of Portfolio Rate y + 2 (D) 52 1f1. SP - 4Q Portfolio Rates iy+2 11.00% (C) 50 (C) 4Q - 3P (C) 8.24% 10.00% 8.00 'Y ~1 (B) 48 9.00% 7.00 5.00 CB) 4P +4Q Investment Year Rates (B) 7.96% z z+l z+2 A bond with coupons equal to 40 sells for P. A second bond with the same maturity value and term has coupons equal to 30 and sells for Q. A third bond with the same maturity value and term has coupons equal to 80. All prices are based on the same yield rate, and an coupons are paid at the same frequency. Determine the price of the third bond. (A) 4P - 4Q (i) The sum of the present values ofa payment of X at the end of 10 years and a ;::2.:.-::-.~:-.: of Y at the end of 20 years is equal to the present value of a payment of X -;-}' a: ::-.= end of 15 years. (ii) X + Y = 100 (iii) i = 5% The following table gives the pattern of investment year and portfolio interest rates over a three-ye~r period, where m = 2 is the time after which the portfolio method is applicable. Calendar Year of Original Investment y An investment of 1000 is made at the beginning of each of calenda, yea:-o ::. :: - :. a:1d z + 2. What is the average annual effective time-weighted rate of reh.:...-=: :'c:-:::= ::.:e=-yea; period?
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