It is False to state that the "present value" of the eventual payments is be $416,987. The correct present value is "$379,078.62.
To calculate the present value of each payment, we can use the formula:
PV = FV / (1 + r)ⁿ
Where:
- PV is the present value
- FV is the future value
- r is the discount rate
- n is the number of periods
In this case, the FV of each payment is $100,000, the r is 10%, and the n is 1, 2, 3, 4, and 5 for the five payments. Plugging these values into the formula,we get:
PV1 = 100,000 / (1 + 0.1)¹ = $90909.0909091
PV2 = 100,000 / (1 + 0.1)² = $82644.6280992
PV3 = 100,000 / (1 + 0.1)³ = $75131.4800902
PV4 = 100,000 / (1 + 0.1)⁴ = $68301.3455365
PV5 = 100,000 / (1 + 0.1)⁵ = $62092.1323059
Adding up the present values of each payment, we get:
Total PV = PV1 + PV2 + PV3 +PV4 + PV5 =
Total PV = 90909.0909091 + 82644.6280992+ 75131.4800902 + 68301.3455365 + 62092.1323059
Total PV = 379078.676941
Total PV ≈ $ 379,079.
Therefore, the present value of the eventual payments is $379,079. which makes the assertion of the officials false.
Full Question:
Although part of your question is missing, you might be referring to this full question:
A parish is sued for sexual harassment resulting in a judgment. The case is settled for $500K to be paid in five annual installments of $100K beginning immediately. In as much as the parish uses a discount rate of 10% to evaluate all long term projects, officials determine the "present value" of the eventual payments to be $416,987. True or False?