Question

Question 4 Not yet answered 4. Frances borrows $10,000 and agrees to make 20 equal annual payments toward principal, where the first payment is due in one year. In addition to the principal repayments, each year she will pay interest at 12% effective on the outstanding principal. The lender wishes to sell the loan to an investor immediately after the loan is made. Determine the sale price such that the investor will achieve a yield of 15% on this investment. Points out of 5.00 P Flag question Select one: a. $8,700 < X < $8,800 b. $8,500 < X < $8,600 c. $8,400< X <$8,500 d. X < $8,400 e. $8,600 < X < $8,700

Answer 1

Total loan amount = $10,000

20 year equal annual installment of the principal = $10000 / 20 = $500

Calculation of the PV of the total installment (principal + interest) paid @15%

Year PV factor @15% Present value ON min Principal Loan Interest Total cash Repayment Outstanding payment @12% outflow $ 10,000.00 1 $ 500.00 $ 9,500.00 $ 1,200.00 $ 1,700.00 2 $ 500.00 $ 9,000.00 $ 1,140.00 $ 1,640.00 3 $ 500.00 $ 8,500.00 $ 1,080.00 $ 1,580.00 4 $ 500.00 $ 8,000.00 $ 1,020.00 $ 1,520.00 5 $ 500.00 $ 7,500.00 $ 960.00 $ 1,460.00 6 $ 500.00 $ 7,000.00 $ 900.00 $ 1,400.00 7 $ 500.00 $ 6,500.00 $ 840.00 $ 1,340.00 8 $ 500.00 $ 6,000.00 $ 780.00 $ 1,280.00 9 $ 500.00 $ 5,500.00 $ 720.00 $ 1,220.00 10 $ 500.00 $ 5,000.00 $ 660.00 $ 1,160.00 11 $ 500.00 $ 4,500.00 $ 600.00 $ 1,100.00 12 $ 500.00 $ 4,000.00 $ 540.00 $ 1,040.00 13 $ 500.00 $ 3,500.00 $ 480.00 $ 980.00 14 $ 500.00 $ 3,000.00 $ 420.00 $ 920.00 15 $ 500.00 $ 2,500.00 $ 360.00 $ 860.00 16 $ 500.00 $ 2,000.00 $ 300.00 $ 800.00 17 $ 500.00 $ 1,500.00 $ 240.00 $ 740.00 18$ 500.00 $ 1,000.00 $ 180.00 $ 680.00 19 $ 500.00 $ 500.00 $ 120.00 $ 620.00 20$ 500.00 $ $ 60.00 $ 560.00 0.869565 $ 1,478.26 0.756144 $ 1,240.08 0.657516 $ 1,038.88 0.571753 $ 869.06 0.497177 $ 725.88 0.432328 $ 605.26 0.375937 $ 503.76 0.326902 $ 418.43 0.284262 $ 346.80 0.247185 $ 286.73 0.214943 $ 236.44 0.186907 $ 194.38 0.162528 $ 159.28 0.141329 $ 130.02 0.122894 $ 105.69 0.106865 $ 85.49 0.092926 $ 68.77 0.080805 $ 54.95 0.070265 $ 43.56 0.061100 $ 34.22 $ 8,625.93

Thus the investor should purchase the investment at $8625.93 in order to earn a yield of 15%.

Thus the answer would be: e. $8,600 < X < $8,700

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