After a protracted legal case, Joe won a settlement that will pay him $11,000 each year at the end of the year for the next ten years. If the ,market interest rates ar currently 5%, exactly how much should the court invest today, assuming end of each year payment, so there will be nothing left in the account after the final payment is made?
To find out how much money the court should invest today, we need to calculate the present value of the future cash flows. In this case, the future cash flows are the annual payments of $11,000 for the next ten years.
The formula to calculate the present value of an annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case:
PMT = $11,000 (annual payment)
r = 5% (interest rate)
n = 10 (number of years)
Now, let's plug in the values and calculate the present value (PV):
PV = $11,000 * (1 - (1 + 0.05)^(-10)) / 0.05
Using a calculator or spreadsheet, the present value can be calculated as follows:
PV = $11,000 * (1 - (1 + 0.05)^(-10)) / 0.05
PV ≈ $11,000 * (1 - 0.61391) / 0.05
PV ≈ $11,000 * (0.38609) / 0.05
PV ≈ $85,792.73
Therefore, the court should invest approximately $85,792.73 today to ensure that there will be nothing left in the account after the final payment is made.