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6 March, 07:54

What is the present value of a series of payments that grow by 10% per year over 5 years. The starting value is $50,000 at the end of year 1. The interest rate (discount rate) is 6%, compounded annually.

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  1. 6 March, 09:12
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    PV = $163,714.68

    Explanation:

    Giving the following information:

    A series of payments grow by 10% per year over 5 years. The starting value is $50,000 at the end of year 1. The interest rate is 6%.

    The easiest way is to include the growing rate in the interest rate, therefore:

    Interest rate = 16%

    First, we need to calculate the final value of the annuity and then the present value:

    FV = {A*[ (1+i) ^n-1]}/i

    A = annual deposit = 50,000

    i = 0.16

    n = 5

    FV = {50,000*[ (1.16^5) - 1]}/0.16 = $343,856.77

    Now, we can calculate the present value:

    PV = FV / (1+i) ^n

    PV = 343,856.77/1.16^5 = $163,714.68
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