Question

Interest rate for an annuity Personal Finance Problem Anna Waldheim was seriously injured in an industrial accident. She sued the responsible parties and was awarded a judgment of $2,000,000. Today, she and her attorney are attending a settlement conference with the defendants. The defendants have made an initial offer of $156,000 per year for 25 years. Anna plans to counteroffer at $255,000 per year for 25 years. Both the offer and the counteroffer have a present value of $2,000,000, the amount of the judgment. Both assume payments at the end of each year.

a. What interest rate assumption have the defendants used in their offer (rounded to the nearest whole percent)?
b. What interest rate assumption have Anna and her lawyer used in their counteroffer (rounded to the nearest whole percent)?
c. Anna is willing to settle for an annuity that carries an interest rate assumption of 9%. What annual payment would be acceptable to her?

Answer 1

a. The defendants have used an interest rate assumption of 6.59% in their offer. b. Anna and her lawyer have used an interest rate assumption of 10.74% in their counteroffer. c. Anna would accept an annual payment of $1,735,905 for 25 years with an interest rate assumption of 9%.

Step-by-step explanation:

a. To determine the interest rate assumption used by the defendants in their offer, we need to find the interest rate that will result in a present value of $2,000,000 for the annual payment of $156,000 for 25 years. Using a financial calculator or spreadsheet, we can find that the interest rate is approximately 6.59%.

b. Similarly, to find the interest rate assumption used by Anna and her lawyer in their counteroffer, we need to find the interest rate that will result in a present value of $2,000,000 for the annual payment of $255,000 for 25 years. Using the same calculation, we find that the interest rate is approximately 10.74%.

c. To find the annual payment that would be acceptable to Anna, we need to find the present value of the payment of $255,000 per year for 25 years using an interest rate assumption of 9%. Again, using a financial calculator or spreadsheet, we find that the present value is approximately $1,735,905.