Please answer these questions:
A. 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?
So I think I need to add them all up seperatly(annually), but do I multiply 11,000 by the 5% ?
You would have to multiply 11,000(1+i)^x for each year. Where i is the interest rate and x is how many years are remaining.
11,000(1.05)^9
11,000(1.05)^8
11,000(1.05)^7
etc., then add the values to find the value of annuity.
To determine how much the court should invest today, you need to calculate the present value of the future cash flows. The present value (PV) is the current value of a future sum of money, taking into account the time value of money.
In this scenario, Joe will receive $11,000 at the end of each year for the next ten years. The market interest rate is 5%. To calculate the present value, you can use the formula for the present value of an ordinary annuity:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value of the annuity
PMT = The annual payment amount
r = Interest rate per period (in this case, 5% or 0.05)
n = Number of periods (in this case, 10 years)
Plugging in the given values, the calculation is as follows:
PV = $11,000 * [1 - (1 + 0.05)^(-10)] / 0.05
PV = $11,000 * (1 - 1.628895) / 0.05
PV = $11,000 * (-0.628895) / 0.05
PV = -$6,918.85
Therefore, the court should invest approximately $6,918.85 today so that after the final payment is made, there will be nothing left in the account. It is important to note that the negative sign indicates an outflow of funds (investment required) rather than an inflow.