Unit 8 Exercise

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?

4. For how many years will Prasad make payments on the $28 000 he borrowed to start his machine shop if he makes payments of $3400 at the end of every three months and interest is 8.08% compounded semi-annually? PV = $28,000; PMT = $3,400; P/Y = 4; C/Y = 2; c = 2/4 = 0.5; I/Y = 8.08; i = 8.08%/2= 4.04% = 0.0404 P = 1.0404 0.5 -1 = 0.02 n = In[(1-(28,000(0.02)/3,400)]/-In(1+0.02) n = In[1-(0.164705882)]/-In (1+ 0.02) n = In (0.835294118)/-In (1.02) n = -0.179971379/-0.019802627 n = 9.08825 = 9 quarters or 1 year and 3 months Or round up to 10 quarters which = 2 years and 6 months, the last payment will be less. Calculator n = 9.0882576 12. Keys Company has a target of establishing a fund of $50 000. If $10 000 is deposited at the end of every six months, and the fund earns interest at 4% compounded quarterly, how long will it take to reach the target? FV = 50,000; PMT = 10,000; P/Y=2; C/Y = 4; c = 4/2 = 2; I/Y=4; i = 4%/4 = 1% = 0.01 p = 1.01 2 -1 = 1.0201-1 = 0.0201 = 2.01% n = In[(50,000(0.0201)/10,000)+1]/In(1+0.0201) n = In(1.1005)/In(1.0201) n = 0.095764622/0.019900662 n = 4.812132 = 5 semiannual periods or 2 years and 6 months the last payment will be less. Calculator = 4.812132 Section 12.5 12. A property worth $35 000 is purchased for 10% down and semi-annual payments of $2100 for 12 years. What is the nominal annual rate of interest if interest is compounded quarterly? Calculator: PV = 31,500 (35,000x10% = 3500 = 35,000-3500); PMT = 2,100; n= 24; p/y = 2; c/y= 4; c = 4/2 = 2 I = 8.2355% or 8.24% rounded

Section 12.6 10. Debbie plans to buy a house for cash instead of paying a mortgage. She is willing to set aside $12 000 at the end of each year for 15 years. She invests the money in a high-risk mutual fund, which has traditionally earned 9.2% annually. Money decreases in value by 2.5% per annum. How much will Debbie have saved after 15 years? What is the accumulated value of the deposits: PMT = 12,000; k=-2.5%= -0.025; n = 15; i=9.2%=0.092 FV = 12,000[(1+0.092) 15 – (1-0.025) 15 /0.092+0.025] FV = 12,000[(3.744032203) - (0.684020686)/0.117] FV = 12,000(3.060011517/0.117) FV=12,000(26.15394459) FV = $313,847.34