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18 April, 20:08

You receive payments at the end of each Quarter starting at the end of Quarter 1 and lasting 6 years (so the last payment you receive is at the end of Quarter 24). These payments are an equal series of payments of $1,000 for all 24 payment periods. The interest rate is 10% APR compounded monthly. What is the present value (at the beginning of Quarter 1) of this series of 24 payments?

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  1. 18 April, 21:17
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    PV = PMT [ (1 - (1 / (1 + r) ⁿ)) / r]

    Where:

    PV = The present value of the annuity

    PMT = The amount of each annuity payment

    r = The interest rate

    n = The number of periods over which payments are to be made

    PV = PMT [ (1 - (1 / (1 + r) ⁿ)) / r]

    = 1000 [ (1 - (1 / (1 + 0.0083) ²⁴)) / 0.0083]

    = 1000 [ (1 - (1 / 1.2194)) / 0.0083]

    = 1000 [ (1 - 0.8201) / 0.0083]

    = 1000 [0.1799‬ / 0.0083]

    = 1000 * 21.6747

    PV = $ 21,674.70

    Explanation:

    Since the annuity is compounded monthly

    r = 10% / 12 = 0.83%

    n = 24
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