Print this out, answer on the papers, then post a scan or photographs of the pap

Question

Print this out, answer on the papers, then post a scan or photographs of the papers. Each question, or part of a question, is worth one point. 1) Mere are the first terms of an infinite geometric series. For each one. state whether or not it has a finite sum. If it does; find it. a) 175, -70, 28, -11.2,... b) -40, 50, -62.5, -78.125... 2) A band signs a deal in which it receives ^$10,000/year in perpetuity. If the average inflation rate into the indefinite future is 4.4%, calculate the real total of this income stream. Round your answer to the nearest ^$100. 3) The eleventh term in an infinite geometric sequence is 80. The fourteenth term in this series is 19.53125. What is the sum of this infinite series? Round your answer to die nearest 0.001 4) Every week the sales of a band's album drop by the same percentage relative to the previous week's sales. In its first week an album sells 8,000 copies. In its seventh week an album sells 2,800 copies. Assuming this trend continues, calculate the total number of albums which will be sold. Round your answer to the nearest album. 5) A woman inherits ^$10,000, and is considering where to invest it. Calculate the annual rates of return for each of the following investments (rounding to the nearest 0.1% where needed). a) She has as ^$15,000 car loan, on which she is charged an annual yield of 7.9%. She could reduce this debt to ^$5,000. Rate of Return: b) She can loan the money to a relative's business, who promises to pay her bake ^$15,000 in 6 years (Assume this loan is safe-she's 100% certain that she'll be paid back.). Rate of Return: c) She can purchase a parking space for her car which costs ^$10,000 (Assume there are no expenses associated with owning it.). Each month she must pay ^$15 in taxes and another ^$15 for maintenance, but she no longer has to pays ^$100 per month to park her car in a garage. Rate of Return: 6) A condo is purchased for ^$200,000. It has monthly taxes of ^$55, fees of ^$315, and other expenses of ^$50. A comparable apartment costs ^$1500 to rent. Five years later, the condo is sold for ^$290,000, but the real estate agent keeps 5% of the selling price. Calculate the total rate of return received by the owner, rounding to the nearest 0.1%. 7) A share of corporate stock pays a dividend to its owner of ^$2/year. This amount is expected to be stable into the indefinite future. If the annual safe yield is stable at 5.75%, what is the value of this share of stock? Round your answer to the nearest cent.

Explanation / Answer

1) Common ratio = -2.5

AS|r|>1 diverges

inf sum = infinity

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Common ratio = 5/4 >1

Hence no finite sum

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3) a11 = ar10 = 80

ar13=19.53125

Divide to have r^3 = 19.53125/80 = 0.244141

=0.244

r = 0.625

a = 80/r^10 = 8796.093

Hence sum of infinite series = 23456.25

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a= 8000

ar^6 = 2800

r^6 = 0.35

r=0.8395

Total sold = 8000/(1-0.8395) = 49838.62

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