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9 January, 04:32

Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $10,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)

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  1. 9 January, 04:39
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    A = $4,838.95 monthly

    Explanation:

    Giving the following information:

    She is currently planning to retire in 30 years and wishes to withdraw $10,000/month for 20 years from her retirement account starting at that time.

    First, we need to calculate the amount needed for retirement:

    FV = 10,000*12*20 = 2,400,000

    Now, we can use the following formula:

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

    A = annual deposit

    Isolating A:

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

    Effective rate = 0.02/12 = 0.0017

    n = 12*30 = 360

    A = (2,400,000*0.0017) / [ (1.0017^360) - 1]

    A = $4,838.95 monthly
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