# Math Help - what am i doing wrong?

1. ## what am i doing wrong?

Find the present value of an annuity that pays $6000 at the end of each 6-month period for 8 years if the interest rate is 8% compounded semiannually. According to my book, the answer is$69,913.77

I don't understand why?
according to my method i get another answer..

An = 6000 [ 1- (1+0.01)^-16/.01 = 90,000

what am i doing wrong?
thanks.

2. Hello, jhonwashington!

Two errors . . .

Find the present value of an annuity that pays $6000 at the end of each 6-month period for 8 years if the interest rate is 8% compounded semiannually. According to my book, the answer is$69,913.77 .
. . . Right!

I don't understand why?
according to my method i get another answer..

An = 6000 [ 1- (1+0.01)^-16/.01 = 90,000 .
. . . Incorrect formula

. . and incorrect interest rate.

The rate is 8% compounded semiannualy: . $i \:=\:\frac{8\%}{2} \:=\:{\color{blue}0.04}$

The formula is: . ${\color{blue}P \;=\;A\,\frac{(1+i)^n - 1}{i(1+i)^n}}$

And we have: . $P \;=\;6000\,\frac{1.04^{16} - 1}{(0.04)(1.04^{16})} \;=\;69,\!913.77365...$