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Thread: Retirement Calculations

  1. #1
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    Retirement Calculations

    I can't figure this out for the life of me:
    1. Rachel deposits $200.00 into her retirement plan each month and the company that she works for deposits half of Rachelís monthly deposits into her retirement plan as well. The retirement plan earns 6% per year, compounded monthly, with an interest rate per period of 0.5% (0.005). Rachel wants to retire in 30 years.

    2. Rachel would have $597,447.00 in her retirement plan if she decided to retire in 40 years instead of in 30 years. How much extra money would Rachel have in her retirement plan by retiring in 40 years instead of in 30 years?

    3. It is important to remember Rachel and her company will only deposit $36,000 into her retirement plan during the extra 10 years if she decided to retire after 40 years instead of 30 years. The rest of the extra money in her account is the result of compound interest. How much of the extra money earned during the extra 10 years is a result of the compounded interest?
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  2. #2
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    Re: Retirement Calculations

    Let A = amount saved per month so A = (200 + 50% of 200) = 300
    Let r = monthly interest gain = 1.005
    After month 1 amount saved = 300*r + 300 (two months deposit of 300 plus 0.5% interest)
    After month 2 amount saved = (300*r + 300)*r + 300 = 300*r^2 + 300*r^1 + 300*r^0
    After month m amount saved = 300*(r^0 + r^1 + r^2 + ... + r^m)

    But the second term is a geometric series. Look up summing geometric series
    So after m months amount saved is 300 * (1-r^m)/(1-r)

    The second part of the question actually gives away a check on your maths
    Put A = 300, r = 1.005 and m = 40*12 and you get 597447.20
    Hope this helps
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  3. #3
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    Re: Retirement Calculations

    end 40th year: 597,447
    end 30th year: 301,355

    Interest = 597447 - 301355 - 120*300 = 260092

    Check: 301355 + 36000 (deposits) + 260092 (interest) = 597447
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