algebra

Tasha invests $5,000 annually at 6% and $5,000 annually at 8%. Thomas invests $10,000 annually at 7%. Which statement accurately compares the two investments if interest is compounded annually?

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  1. I do not see the statements

    .5*(1.06)^n + .5(1.08)^n
    compared to
    1 * (1.07)^n

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  2. Each person will have exactly the same amount over time because each invested $10,000 at an average interest rate of 7%.

    Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

    Thomas’s investment will yield more from the start because he has more money invested at the average percentage rate.

    Tasha’s investment will be greater at first because she invested some at a higher rate, but Thomas’s investment will be greater over the long run.

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  3. well, look after a year

    .5*1.06 + .5*1.08 = 1.07

    1 * 1.07 = 1.07

    look after 5 years
    .5(1.06)^5 + .5(1.08)^5 = 1.403776827
    1.07^5 =1.402551731 less

    look after 20 years
    .5*1.06^20 + .5*1.08^20 = 3.9340463
    1.07^20 = 3.869684462 less
    Tasha wins because the 8% half makes the Tasha investment grow faster

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