You have a chance to buy an annuity that pays $1100 at the end of each year for 3 yeas. You could earn 3% on your money in other investments with equal risk. What is the most you should pay for the annuity?
To determine how much you should pay for the annuity, you need to calculate the present value of the future cash flows. The formula for present value is:
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n
Where:
PV = Present Value (the amount you should pay for the annuity)
CF = Cash Flow (the amount you will receive each year)
r = Interest rate (3% or 0.03 in this case)
n = Number of periods (3 years in this case)
Now let's plug in the values into the formula:
PV = $1100 / (1 + 0.03)^1 + $1100 / (1 + 0.03)^2 + $1100 / (1 + 0.03)^3
Calculating this, we get:
PV = $1100 / (1.03) + $1100 / (1.03)^2 + $1100 / (1.03)^3
PV = $1067.96 + $1035.95 + $1004.03
Adding these values together, we get:
PV = $3107.94
Therefore, the most you should pay for the annuity is $3107.94.