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
how tf i do this
PV = 2000((1 - 1.06)^-14)/.06
= 18589.97
To find the present value of an ordinary annuity, we can use the formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value
PMT = Payment per period
r = interest rate per period
n = number of periods
In this case, the payment per semiannual period (PMT) is $2,000, the interest rate per semiannual period (r) is 12%/2 = 6%, and the number of semiannual periods (n) is 7*2 = 14.
Using these values, we can calculate the present value:
PV = $2,000 * [(1 - (1 + 0.06)^(-14)) / 0.06]
PV ≈ $15,616.10
Therefore, the present value of the ordinary annuity is approximately $15,616.10.
To find the present value of an ordinary annuity, you can use the formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value of the annuity
PMT is the periodic payment
r is the interest rate per period
n is the total number of periods
In this case, the periodic payment is $2,000, the interest rate per period is 12% divided by 2 (since it's compounded semiannually), and the total number of periods is 7 years multiplied by 2 (since it's semiannual payments).
Let's plug in the values and calculate:
PMT = $2,000
r = 12% / 2 = 0.12 / 2 = 0.06 (6% per semiannual period)
n = 7 * 2 = 14 periods
PV = $2,000 * (1 - (1 + 0.06)^(-14)) / 0.06
Calculating this, we get:
PV ≈ $2,000 * (1 - 1.336569) / 0.06
PV ≈ $2,000 * (-0.336569) / 0.06
PV ≈ -$6,731.38 / 0.06
PV ≈ -$112,189.63
Rounding the answer to the nearest cent:
PV ≈ -$112,189.63 ≈ -$112,189.63
Therefore, the present value of the ordinary annuity is approximately -$112,189.63.