Find the present value of the ordinary annuity. Please round the answer to the nearest cent.$2,000 per semiannual period for 7 yr at 12%/year compounded semiannually
PV = 2000 (1 - 1.06^-14)/.06
= ....
To find the present value of an ordinary annuity, you can use the formula:
PV = P * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
P = Payment per period
r = Interest rate per period
n = Number of periods
In this case:
P = $2,000 per semiannual period
r = 12%/year compounded semiannually, so the interest rate per semiannual period is 6% (12%/2)
n = 7 years, but since the payments are semiannual, the number of periods is 7 * 2 = 14
Now, let's plug these values into the formula:
PV = $2,000 * [(1 - (1 + 0.06)^(-14)) / 0.06]
Calculating this expression:
PV = $2,000 * [(1 - (1.06)^(-14)) / 0.06]
PV = $2,000 * [(1 - 0.476091) / 0.06]
PV = $2,000 * [0.523909 / 0.06]
PV = $2,000 * 8.73182
PV = $17,463.64
The present value of the ordinary annuity is approximately $17,463.64.