To solve this we are going to use the present value of annuity formula:
where
is the present value
is the periodic payment
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of payments per year
is the number of years
We know from our problem that
and
. To convert the interest rate to decimal form, we are going to divide it by 100%:
Since the interest is compounded semiannually, it is compounded 2 times per year; therefore,
. Similarly, since the payment is made at the end of each 6 months, it is made 2 times per year; therefore,
.
Lest replace the values in our formula:
We can conclude that the correct answer is <span>
$72,634.83</span>