# Math

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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 - ,

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.