After a protracted legal case, Joe won a settlement that will pay him $11,000 each 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 how much the court should invest today, we need to use the concept of present value. Present value is the current value of a future stream of cash flows, taking into account the time value of money. In this case, the future cash flows are the annual payments of $11,000, and the market interest rate is 5%.
To find the present value, we can use the formula:
Present Value = Cash Flow / (1 + Interest Rate)^n
In this formula, "Cash Flow" represents the annual payment of $11,000, "Interest Rate" is the market interest rate of 5%, and "n" represents the number of periods (in this case, years). We have a total of ten payments, so n = 10.
Now let's plug in the values and calculate the present value:
Present Value = $11,000 / (1 + 0.05)^10
To simplify the calculation, let's first solve (1 + 0.05)^10:
(1 + 0.05)^10 = 1.05^10 ≈ 1.6289
Now we can calculate the present value:
Present Value = $11,000 / 1.6289 ≈ $6,763.03
Therefore, the court should invest approximately $6,763.03 today to ensure there is nothing left in the account after the final payment is made.