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24 February, 04:08

The Mendes family bought a new house 8 years ago for $126,000. The house is now worth $156,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Round your answer to the nearest tenth of a percent (1.2% etc)

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  1. 24 February, 04:34
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    Rate of appreciation is based on an exponential function, i. e.

    if r=rate of appreciation, after n years, the new value is

    F=P (1+r) ^n.

    P=present worth

    F=future worth.

    Here,

    P=126000

    F=156000

    n=8

    so

    156000=126000 (1+r) ^8

    =>

    (1+r) ^8 = (156000/126000) = 26/21

    =>

    (1+r) = (26/21) ^ (1/8) = 1.02706 (approx.)

    =>

    r=1.02706-1=0.02706, or

    rate of appreciation is approximately 2.7%
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