what am i doing wrong?

**jhonwashington** · May 7th 2009, 11:35 AM

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.

**Soroban** · May 7th 2009, 01:28 PM

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

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