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Math Help - Annuity problem? Please Help!

  1. #1
    lionking
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    Exclamation Annuity problem? Please Help!

    Matthew deposits $150 each month in his account for 10 years. How much would he have after the 10 year period if the bank pays 6% p.a. interest compounded on a half yearly basis? (Sow all Working)

    Heres what i got so far . . .

    150 x { (1 + 0.03) to the power of 120 - 1 }
    ------------------------------------------ =
    0.03
    But i'm not sure if i get the right answer . . .
    do i half the interest rate to 0.03?
    and do I put 120 time periods for ( 10 years x 12 months) the amount of deposits or 20 time periods for (10 years x 2 = 20 half years) . . . ?

    Thankyou if you help or for trying to help . . . i gtg to bed so yeah someone please be really smart on right now . . . .
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  2. #2
    Super Member

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    Hello, lionking!

    Matthew deposits $150 each month in his account for 10 years.
    How much would he have after the 10-year period if the bank pays 6% p.a.
    interest compounded on a half-yearly basis?
    Don't let his monthly deposits confuse you.

    Since the bank looks at his account every six months,
    . . it is as if he deposits: 6 \times \$150 \:=\:\$900 semi-annually.

    The periodic interest rate is: \frac{6\%}{2} = 0.03
    . .and there are: 10 \times 2 \:=\:20 periods.

    The final amount is: . A \;=\;900\,\frac{1.03^{20} -1}{0.03} \;\approx\;\$24,183.34

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