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Math Help - Reconcile two different ways to calculate a discount rate for present value

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    Reconcile two different ways to calculate a discount rate for present value

    A colleague and I are in disagreement on the correct way to calculate a discount rate for a present value equation and would like an opinion from some more knowledgeable folks.

    I have a single data point that a dollar today will be worth $0.22 after 24 months. Given the present value equation: PVi = 1 / ( 1 + r ) ^ i ...

    A) That is a rate of 78% over 24 months, so the monthly compounded rate is (1+.78)(1/24) - 1 = 0.024316, thus the discount rate (r in the PV equation) is 0.024316.

    or

    B) By plugging in 0.22 for PVi and 24 for i, we can rewrite the PV equation to solve for r as 1 - (1 / 0.22)(1/24) = 0.06512, thus the discount rate (r in the PV equation) is 0.06512.

    Both these approaches seem valid to me, but obviously they will result in very different answers for Present Value. A) would give a PV24 of 0.56 per dollars and B) gives a value of 0.22 per dollar.

    Can anyone help me figure out which approach is the correct one?
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    Re: Reconcile two different ways to calculate a discount rate for present value

    So you are expecting a sharp deflation after many years of inflation? Or do you mean an increase of $0.22 so that, after two years, a dollar will be worth $1.22?
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    Re: Reconcile two different ways to calculate a discount rate for present value

    I suppose it most closely resembles inflation. So $1 in month 24 is worth $0.22 today.
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    Re: Reconcile two different ways to calculate a discount rate for present value

    A) That is a rate of 78% over 24 months, so the monthly compounded rate is (1+.78)(1/24) - 1 = 0.024316, thus the discount rate (r in the PV equation) is 0.024316.
    you are not given a rate of 78% spread over 24 months. Your 0.22 will accumulate to $1. that is a accumulation of about 400% over 24 months.
    you have solved for the interest rate in b.
    Last edited by SpringFan25; April 27th 2012 at 01:41 PM.
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    Re: Reconcile two different ways to calculate a discount rate for present value

    Quote Originally Posted by odonnellphil View Post
    I suppose it most closely resembles inflation. So $1 in month 24 is worth $0.22 today.
    Why in heck don't you use something CLEAR...
    You are asking about PV calculations, not inflation or whatever, right?

    $85 in a savings account accumulates to $100 after 2 years, at rate of P% compounded annually.
    What is P?
    You have 2 ways of calculating P? ... or what are you asking?
    Last edited by Wilmer; April 27th 2012 at 08:24 PM.
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