MA170wk2solns

# Total cost total interest that he must pay for

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(b) What is the cost to Jacob for taking the loan? total cost = total interest that he must pay for borrowing the money Total interest: \$ 26 : 85 + \$46 : 51 + \$31 : 64 = \$105 : 00 in total (c) Would Jacob be better or worse off if he had to pay interest on the entire principal, but not until the loan is paid off (Dec 1)? Why? (No additional calculations are needed.) He would be worse off because in most of October and all of November he’d be paying interest on \$5000 rather than on the smaller amounts still owing. 2. [7 marks ] A sum of \$2000 was deposited into a fund on February 4th. (a) If on November 6th of the same year, the balance of \$2036 was withdrawn, what was the interest rate? Assume that ordinary simple interest is used. Express your answer as a percentage to 1 decimal place. # days: 310 ° 35 = 275 I = P rt 36 = 2000 r ° 275 360 ± = 13 750 9 r r = 36 (9) 13750 = 162 6875 : = 0 : 02356 4 = 2 : 4% OR S = P (1 + rt ) 2036 = 2000 ° 1 + r ° 275 360 ±± = 13 750 9 r + 2000 r = 9 (2036 ° 2000) 13750 = 162 6875 : = 0 : 02356 4 = 2 : 4% 1

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(b) If the interest rate is r = 10% how many days will it take to earn at least \$50.00 in interest? Your answer should be a whole number. (Assume exact simple interest is used.) I = P rt 50 = 2000 (0 : 1) ° t 365 ± = 200 t 365 t = 365 (50) 200 = 219 670 = 365 4 : = 91 : 25 : = 92 days 3. [4 marks ] A °ve year investment grows according to the amount function S ( t ) = 150 + 0 : 75 t 2 : Determine (a) the principal; P = S (0) = 150 + 0 : 75 (0) 2 = \$150 : 00 (b) the accumulated value of the investment after 2 years; S (2) = 150 + 0 : 75 ² 2 2 ³ = \$153 : 00 (c) I 4 ;
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