Posted by **Anonymous** on Wednesday, November 14, 2007 at 6:25pm.

please explian how to figure this out thanks :)

How much money must be deposited now at 6% interest compounded semi-annually, to yelid an annuity payment of $4,000 at the beginning of each six-month peroid for a total of five years I need to then round my answer to the nearest cent

- Math -
**tchrwill**, Wednesday, November 14, 2007 at 7:24pm
How much money must be deposited now at 6% interest compounded semi-annually, to yelid an annuity payment of $4,000 at the beginning of each six-month peroid for a total of five years I need to then round my answer to the nearest cent

The present value of an annuity that willpay out $4000 at the end of every 6 month period (not including the first day of the 5 year period) paying 6% compounded semi-annually derives from P = R[1 - (1 + i)^-n)]/i where P = the present value, R = up front deposit, i = the decimal periodic interest rate, and n = the number of interest bearing periods.

Therefore, P = 4000[1 - (1 + .03)^10)]/.03 = $34, 121.

The present value of an annuity that will pay out $4000 at the beginning of every 6 month period paying 6% compounded semi-annually would be

P = 4000[1 - (1 + .03)^-9)]/.03 = $31,144 + $4000 = $35,144. In this case the present value loses $4000 at the start of the 5 year period before any interest is gained and only 9 interest bearing periods remain.

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