After a protracted legl 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 are currently 5%, exactly how much should the court invest today, assuming end of year payments, so there will be nothing left in the account after the final payment is made?
To calculate the amount that should be invested today, we need to use the present value formula. The present value formula allows us to determine how much money needs to be invested now to achieve a specific future value.
The present value formula is:
PV = FV / (1 + r)^n
Where:
PV = Present value (amount to be invested today)
FV = Future value (amount to be received each year for the next ten years)
r = Interest rate
n = Number of years
In this case, Joe will receive $11,000 at the end of each year for the next ten years, and the interest rate is 5%.
Let's plug the values into the formula and solve for PV:
PV = $11,000 / (1 + 0.05)^10
Calculating this expression will give us the present value that needs to be invested today to achieve the desired future value.