# Annuity problem? Please Help!

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• Mar 6th 2008, 05:59 AM
lionking
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 (Yawn) someone please be really smart on right now . . . . • Mar 6th 2008, 06:35 AM Soroban Hello, lionking! Quote: 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: . $A \;=\;900\,\frac{1.03^{20} -1}{0.03} \;\approx\;\24,183.34$