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Math Help - ammount of an annuity2

  1. #1
    Senior Member euclid2's Avatar
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    ammount of an annuity2

    You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have $200,000 at the time of your last deposit? (Hint: You need to find the value for "a". )
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  2. #2
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    Quote Originally Posted by euclid2 View Post
    You wish to purchased a house for $200,000 in 12 years. You can invest your money at 5%/a compounded semiannually. How much do you need to invest every 6 months, starting in 6 months, so that you will have $200,000 at the time of your last deposit? (Hint: You need to find the value for "a". )
    It is an increasing annuity with

    Rent, R = ?

    Future value, F = $200 000

    interest, i = \frac{5}{2}\% = 0.025

    number of pay periods, n = 12 \times 2 = 24

    Future value, F = \frac {(1+i)^n - 1}{i} \times R

    200 000 = \frac {(1.025)^{24} - 1}{0.025} \times R

    R = \frac{200 000 \times 0.025}{(1.025)^{24} - 1}

    R = $6182.56
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