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math!

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3. Suppose that Jill, at age 24, decides to invest $200 monthly into a portfolio that earns 7% compounded monthly and does this until she turns 34. At age 34 she stops contributing to her portfolio, and just lets it gain the same interest (7% compounded monthly) until she retires at age 67.

Now suppose that Mark (the same age as Jill) decides to unwisely procrastinate investing a portion of his income until he turns 34 years old. At this point in his career, he decides to consistently invest $200 monthly (7% compounded monthly until he retires at age 67.

a) How much will both have at age 67 for retirement?
Jill _____________ Mark _____________

b) How much of their final investment is their own money that they contributed (principal)?
Jill _____________ Mark _____________

  • math! - ,

    JILL:
    monthly rate = .07/12 = .0058333... (I stored that for full accuracy)
    for 10 years ----> n = 120

    amount after 10 years = 200( 1.0058333..^120 - 1)/.00853333.
    = $34616.96
    Now that sits for 33 years or 396 months and at the end of that will have a value of
    34616.96(1.0085333..)^396
    = $346,413.20

    Mark:

    invests $200 for 396 months
    amount = 200(1.00853333..^396 - 1)/.0085333
    = $308,812.68

    Jill used 200x120 or $24.000 of her own money
    Mark used 200x396 or $79,200 of his own, but ends up with less

    Behold, the power of compound interest and time.

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