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Math Help - Solving Time value of money

  1. #1
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    Lightbulb Solving Time value of money

    Hi all,

    I'm currently preparing for CFA lvl 1 exams. My maths got rusty. Although it is allowed to use financial calculator, i want to know how to solve this manually, here goes...

    (100/(1)) + (100/(1+r)^1) + (100/(1+r)^2 = 250

    Solve R.

    Thanks in advance!
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  2. #2
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    Re: Solving Time value of money

    Start by getting a common denominator.
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  3. #3
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    Re: Solving Time value of money

    Quote Originally Posted by Prove It View Post
    Start by getting a common denominator.
    Hi, do you mean via trial and error?

    Can show me how is it done?

    Many thanks.
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  4. #4
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    Re: Solving Time value of money

    Definitely not by trial and error.

    \displaystyle \begin{align*} 100 + \frac{100}{1 + r} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2}{(1 + r)^2} + \frac{100(1 + r)}{(1 + r)^2} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2 + 100(1 + r) + 100}{(1 + r)^2} &= 250 \\ 100(1 + r)^2 + 100(1 + r) + 100 &= 250(1 + r)^2 \end{align*}

    Now expand everything, collect like terms, set equal to 0 and solve the resulting quadratic.
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  5. #5
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    Re: Solving Time value of money

    Quote Originally Posted by Prove It View Post
    Definitely not by trial and error.

    \displaystyle \begin{align*} 100 + \frac{100}{1 + r} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2}{(1 + r)^2} + \frac{100(1 + r)}{(1 + r)^2} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2 + 100(1 + r) + 100}{(1 + r)^2} &= 250 \\ 100(1 + r)^2 + 100(1 + r) + 100 &= 250(1 + r)^2 \end{align*}



    Now expand everything, collect like terms, set equal to 0 and solve the resulting quadratic.
    Hi, Thanks!

    Would you mind show me the rest of the steps to solve R?
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  6. #6
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    Re: Solving Time value of money

    Quote Originally Posted by kelxktyc View Post
    Hi, Thanks!

    Would you mind show me the rest of the steps to solve R?
    Yes I would mind. It is against the rules to complete work for a student that is supposed to count for their grade. You are expected to show some effort.
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