algerbra

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Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:



Number of years 1 2 3
Option 1 (amount in dollars) 1300 1600 1900
Option 2 (amount in dollars) 1120 1254.40 1404.93


Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Which option should Belinda choose? Explain your answer, and show the investment value after 20 years for each option. (4 points)

  • algerbra -

    A)
    Option 1 is linear, $300 per year

    Option 2 , exponential is compound interest, a geometric sequence
    an = an-1 * 1.12

    B)
    Option 1
    A = 1300 + 300(n-1) = P +.23 P (n-1)
    Option 2
    A = 1120 * 1.12^(n-1) = P *1.12^(n-1)

    C) after 20 years
    Option 1
    P + .23*19 P = 5.37 P
    Option 2
    P* 1.12^19 = 8.61 P
    so despite the lower percentage, the compounding wins big time.

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