Math
posted by Anonymous on .
please explian how to figure this out thanks :)
How much money must be deposited now at 6% interest compounded semiannually, to yelid an annuity payment of $4,000 at the beginning of each sixmonth peroid for a total of five years I need to then round my answer to the nearest cent

How much money must be deposited now at 6% interest compounded semiannually, to yelid an annuity payment of $4,000 at the beginning of each sixmonth 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 semiannually 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 semiannually 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.