Question

You are offered a court settlement in the following terms: you will receive 6 equal payments of $4,546 each every year, with the first payment being made 2 years from now. The current annual interest rate is 5%. Assume yearly compounding. What is this settlement worth in present value terms? Enter your answer in the form of dollars, rounded to the nearest cent, and without the dollar sign ('$').

Answer 1

The present value of the court settlement is approximately $20,912.51.

Step-by-step explanation:

To calculate the present value of the court settlement, we need to discount each payment back to its present value using the formula PV = PMT / (1 + r)^n, where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of years. In this case, the payment amount is $4,546, the interest rate is 5%, and the number of years is 6.

Using the formula, the present value of each payment is:

1. $4,546 / (1 + 0.05)^2 ≈ $4,110.41
2. $4,546 / (1 + 0.05)^3 ≈ $3,723.61
3. $4,546 / (1 + 0.05)^4 ≈ $3,393.97
4. $4,546 / (1 + 0.05)^5 ≈ $3,115.21
5. $4,546 / (1 + 0.05)^6 ≈ $2,881.84
6. $4,546 / (1 + 0.05)^7 ≈ $2,687.47

To find the present value of the court settlement, we sum up the present values of all the payments:

Present Value = $4,110.41 + $3,723.61 + $3,393.97 + $3,115.21 + $2,881.84 + $2,687.47 ≈ $20,912.51