Find the present value of an ordinary annuity of $1,400 payments each made semiannually over 8 years and earning interest at 12% per year compounded semi-annually.
$6,954.70
$9,763.58
$14,148.25
$3,365.99
Thanks for the help
To find the present value of an ordinary annuity, you can use the formula:
PV = PMT * (1 - (1+r)^(-n)) / r
where:
PV = Present value of the annuity
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case, the payment amount is $1,400, the interest rate is 12% per year compounded semi-annually, and the number of periods is 8 years (with semiannual payments, this is equivalent to 16 periods).
First, we need to convert the annual interest rate to the semiannual interest rate. Since interest is compounded semi-annually, the interest rate per semiannual period is half of the annual rate. Therefore, the semiannual interest rate is 12% / 2 = 6% = 0.06.
Now, plug the values into the formula:
PV = $1,400 * (1 - (1+0.06)^(-16)) / 0.06
Calculating this expression gives us:
PV = $1,400 * (1 - 0.569516775) / 0.06
PV = $1,400 * (0.430483225) / 0.06
PV = $9,732.44911
Rounding to the nearest cent, the present value of the annuity is approximately $9,732.45.
Therefore, the correct answer is not listed among the given options.