Find the value of the annuity.
a1=8000
I=0.08
N=20
To find the value of the annuity, we can use the formula for the present value of an ordinary annuity:
PV = a1 * (1 - (1 + I)^(-N)) / I
Where:
- PV is the present value of the annuity
- a1 is the initial payment or cash inflow per period (in this case, $8000)
- I is the interest rate per period (in this case, 0.08 or 8%)
- N is the total number of periods (in this case, 20)
Now, let's substitute the given values into the formula:
PV = 8000 * (1 - (1 + 0.08)^(-20)) / 0.08
Calculating this out gives:
PV = 8000 * (1 - 1.99993718264) / 0.08
PV = 8000 * (-0.99993718264) / 0.08
PV = -7999.4974611472 / 0.08
PV ≈ -99,993.71827
The present value of the annuity is approximately -$99,993.72. It appears to be negative, which means the annuity results in a net cash outflow of $99,993.72 over the 20 periods.