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 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?

Question

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 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?

Answer 1

To calculate the initial investment amount that the court should make, we need to determine the present value of Joe's settlement payments. The present value represents the current value of future cash flows, taking into account the time value of money.

In this case, we can use the formula for the present value of an ordinary annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

Where:
PV is the present value
PMT is the annual payment amount
r is the interest rate as a decimal
n is the number of payment periods

Substituting the given values:
PMT = $11,000
r = 5% = 0.05
n = 10

PV = $11,000 x (1 - (1 + 0.05)^(-10)) / 0.05

Let's calculate the present value using the formula:

PV = $11,000 x (1 - (1.05)^(-10)) / 0.05

Now, compute the expression within the parentheses first:

(1.05)^(-10) = 0.613913686
Subtract this value from 1:
1 - 0.613913686 = 0.386086314

Now divide this result by the interest rate of 0.05:
0.386086314 / 0.05 = 7.72172629

Finally, multiply this result by the annual payment amount of $11,000:
7.72172629 x $11,000 = $84,939.99

Hence, the court should invest approximately $84,940 today in order to have enough funds to pay Joe $11,000 each year for the next ten years, assuming an interest rate of 5%.