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 $1,000,000. Today, she and her attorney are attempting a settlement conference with the defendants. The defendants have$124,made an initial offer of $72,649 per year for 30 years. Anna plans to counteroffer at $124,144 per year for 30 years. Both the offer and the counteroffer have a present value of $1,000,000, the amount of the judgment. Both assume payments at the end of each year.

a) what interest rate assumption have the defendents used in their offer (round to nearest whole percent) = 6%

b)what interest rate assumption have Anna and her lawyer used in their counteroffer (round to nearest whole perecent)? =12%

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?

C: If Anna is willing to settle for an annuity that carries an interest rate assumption of 9%, she would be willing to accept an payment of $...............(round to the nearest dollar). My answer of $97,336 was incorrect. What is the correct answer for this problem?

Thanks for your help!

Answer 1

Where,

R = Annual Payment

i = rate of interest

n = no. of periods

When you solve it you will get,

$1,000,000 = R (10.27365)

R = $1,000,000 / 10.27365

R = $97,336

Your answer to the problem is correct.

Still if you want to verify, just do a reverse calculation

Put the value of R in the equation and see whether the LHS = RHS

Note: In the above table I have taken cash flow at the beginning of the year as 0, because problem clearly states that "Both assume payments at the end of each year." So we do not add that 1 to the total of pv factor.