Question

You are offered a court settlement in the following terms: you will receive 8 equal payments of $9,940 each every year, with the first payment being made 4 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 calculated by discounting each of the 8 annual payments of $9,940 at a 5% interest rate, starting from 4 years into the future. We use the present value formula for each payment and sum the totals to find the settlement's current worth.

Step-by-step explanation:

To calculate the present value of the court settlement, we need to discount each of the 8 equal payments of $9,940 by the annual interest rate of 5%, compounded yearly. We will use the present value of an annuity formula for the calculation. Since the first payment is made 4 years from now, the calculation must start from that point.

For each payment, the present value (PV) formula is: PV = P / (1 + r)^n, where P is the payment amount, r is the interest rate per period, and n is the number of periods until the payment is received.

Here's the step-by-step calculation:

1. 
   
3. Identify the payment value (P) which is $9,940.
4. 
   
6. Determine the discount rate (r) per period, which is 0.05 (5% annual interest).
7. 
   
9. Calculate the present value for each payment, with the number of periods (n) corresponding to 4-11 years for each subsequent payment.
10. 
    
12. Sum the present values of all 8 payments to find the total present value of the annuity.

The present value of each payment decreases the further away in the future it is because the discounting effect compounds over time.

To find the present value, use this formula for each of the years (4 through 11), sum all the calculated present values, and that will give you the total present value of the settlement.