200,000=R*[1-(1+0.025)^(-40)]/0.025) Solve for R?

200,000=R*[1-(1+0.025)^(-40)]/0.025)

Solve for R?

2 Answers

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  • 4 years ago
    Favorite Answer

    200,000 = r * [1 - (1 + 0.025)^(-40) ] / 0.025

    First, let's convert those decimals into fractions:

    200,000 = r * [1 - (1 + 1/40)^(-40) ] / (1/40)

    Division of fractions is the same as the multiplication of the reciprocal, so:

    200,000 = r * [1 - (1 + 1/40)^(-40) ] * 40/1

    200,000 = 40r * [1 - (1 + 1/40)^(-40) ]

    Now let's divide both sides by 40:

    5000 = r * [1 - (1 + 1/40)^(-40) ]

    Now let's simplify the fraction sum in the center:

    5000 = r * [1 - (40/40 + 1/40)^(-40) ]

    5000 = r * [1 - (41/40)^(-40) ]

    Next, let's resolve the negative exponent by finding the reciprocal:

    5000 = r * [1 - (40/41)^(40) ]

    We're going to have a 65 digit number if we actually determine 40^40, so at this point, I'll get a decimal approximation to 40/41, then use that to raise to the 40th power. While I'll be rounding writing numbers below, I won't be rounding in the calculator to limit rounding errors:

    5000 ≈ r * (1 - 0.97561^40)

    5000 ≈ r * (1 - 0.3724306)

    5000 ≈ r * (0.6275694)

    Now divide both sides by that decimal (remember, I still have the non-rounded value in my calculator, so you may get different results if you don't do the same):

    r ≈ 5000 / 0.6275694

    r ≈ 7967.24663 (rounded to 5DP)

  • 4 years ago

     

    DELETED QUESTION:

    Determine f(-0.5) and f(1.5) from the following graph?

    http://imgur.com/oHrdPtE

    ——————————————————————————————

    ANSWER:

    Graph has vertex (1,4)

    f(x) = a(x−1)² + 4

    Graph passes through point (0,1)

    1 = a(0−1)² + 4

    1 = a + 4

    a = −3

    f(x) = −3(x−1)² + 4

    f(−0.5) = −3(−0.5−1)² + 4 = −6.75 + 4 = −2.75

    f(1.5) = −3(1.5−1)² + 4 = −0.75 + 4 = 3.25

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