Jessie won a lottery and was given the following choice.He could either take $5000 at the end of each month for 25 years,or a lump sum of $700 000.Assuming annual compounding at approximately what interest rate would he would be indifferent between the two choices?
A)12.3
B)6)7
C)7)0
D)7)3

Question

Quizplus · Accepted Answer

To find the interest rate at which Jessie would be indifferent between the two choices, we need to compare the present value of the annuity (receiving $5000 at the end of each month for 25 years) with the lump sum amount of $700,000. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment amount, r is the monthly interest rate, and n is the total number of payments. Since the payments are monthly and the compounding is annual, adjustments are needed to align the compounding period with the payment period, or an equivalent annual rate can be calculated that matches the present value of the annuity to the lump sum. Through financial calculations or using a financial calculator, it can be determined that an approximate interest rate that makes Jessie indifferent to the choices is around 7.3%, which corresponds to choice D.

Jessie Won a Lottery and Was Given the Following Choice