Unit 8 Exercise

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BUSI 1003-24W-O-A – Math for Business Unit 8 Exercise Stephanie Motyka Yorkville University Prof. Don Moore Monday, February 26, 2024 Chapter 12
Section 12.1 8. Mrs. Cook made deposits of $950 at the end of every 6 months for 15 years. If interest is 3% compounded monthly, how much will Mrs. Cook have accumulated 10 years after the last deposit? PMT=950 i = 3%/12= 0.25%=0.0025 c = 12/2 = 6 n = 15 (2) = 30 p = (1+0.0025) 6 -1 = 0.015094063 FV g = 950[(1+0.015094063) 30 -1/0.015094063] FV g =950(37.59304048) FV g = $35,713.39 FV = PV (1 + i) n FV = 35,713.39 (1+0.0025) (12x10=120) FV = 35,713.39 (1.349353547) FV = $48,189.99 10. Clark’s younger brother saved $18 per month from his paper route for the past two years. If interest is 4% compounded quarterly, how much will he have accumulated in his savings account? PMT = 18; i = 4%/4 = 1% = 0.01; c = 4/12 = 0.333333; n = 2(12)= 24 P =(1+0.01) 0.333333 -1 = 0.003322284 FV g = 18[(1+0.003322284) 24 -1/0.003322284] FV g = 18(24.93968518 FV g = 448.91 Section 12.2 6. A car was purchased for $1500 down and payments of $265 at the end of each month for four years. Interest is 9% compounded quarterly. a. What was the purchase price of the car? PMT = 265; n = 12(4)=48; i = 9%/4 = 2.25% = 0.0225; c = 4/12 = 1/3 = 0.333333 p = (1+0.0225) 0.333333 -1 = 0.007444443 PV g = 265[1-(1+0.007444443) -48 /0.007444443] PV g = $10,662.53 $10,662.53 + $1,500 = $12,162.53 was the purchase price of the car. b. How much interest will be paid?
1500 + [(265 x 12) x 4] = $14,220 =14,220 – 12,162.53 = $2,057.47 is the total interest 8. Langara Woodcraft borrowed money to purchase equipment. The loan is repaid by making payments of $924.37 at the end of every three months over seven years. If interest is 7.3% compounded annually, what was the original loan balance? PMT = 924.37; n = 4(7)=28; i = 7.3%/1 = 7.3% = 0.073; c = ¼ = 0.25 P = (1+0.073) 0.25 -1 = 0.017770668 PV g = 924.37[1-(1+0.017770668) -28 /0.017770668 PV g = $20,251.97 Section 12.3 4. What payment made at the end of each year for 18 years will amount to $16 000 at 4.2% compounded monthly? FV = 16,000; n = 18(1) = 18; p/y = 1; c/y = 12; c = 12/1 = 12; i/y = 4.2; i = 4.2%/12 = 0.35% = 0.0035 P = 1.0035 12 -1 = 1.042818007 – 1 = 0.042818007 = 4.2818% PMT= 16,000(0.042818007)/1.042818007 18 -1 PMT = $607.92 12. An investment fund that pays quarterly dividends for 10 years yields an annual return of 6.6%. If the initial price of the fund is $200, what is the amount of the dividend? PV = 200; n = 10(4) = 40; p/y = 4, c/y = 1; c = ¼ = 0.25; i/y = 6.6; i = 6.6%/1 = 6.6 = 0.066 P = 1.066 0.25 -1 P = 0.016106668 PMT = 200(0.01610668)/1-(1 + 016106668) -40 PMT = 3.221333519/0.472250351 PMT = $6.82 Section 12.4 Continued on next page……………. Section 12.4
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