At the beginning of each year for 5 years, Cindy invests in a mutual fund with a

Question

At the beginning of each year for 5 years, Cindy invests in a mutual fund with an average annual return of ‘r’. The first year she invests $10, the second year $20, the third year $30, the forth year $40 and the fifth year $50. If we assume that x = 1 + r, then at the end of the first year (just before next investment) the value is 10x dollars. Because $20 is then added to the 10x dollars, the amount at the end of second year will be (10x + 20)x dollars and so on. Find:

a. A polynomial in ‘x’ that represents the value of the investment at the end of the fifth year.

b. How much money will Cindy have after 5 years if r = 8%?

Explanation / Answer

a) Value of investment = 10 x^5 + 20x^4 + 30x^3 + 40x^2 + 50x b) Just replace x by 1.08 and you get what you need 10(1.08)^5 + 20(1.08)^4 + 30(1.08)^3 + 40(1.08)^2 + 50(1.08) = 180.350... Please, rate! Thank you.

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