Final answer:
To calculate the most you should pay for the annuity, use the present value formula for an annuity. Plug in the values of the annuity payments and the interest rate to calculate the present value. The present value of the annuity is $224,195.57.
Step-by-step explanation:
To determine the most you should pay for the annuity, we need to calculate the present value of the annuity payments. Since the annuity pays $18,200 at the end of each year for 20 years and you can earn 5% on your money in other investments with equal risk, we will use the present value formula for an annuity:
Present Value = Payment Amount x ((1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate)
Plugging in the values, we get:
Present Value = $18,200 x ((1 - (1 + 0.05)^(-20)) / 0.05) = $18,200 x (1 - (1.05)^(-20)) / 0.05 = $18,200 x (1 - 0.376889064) / 0.05 = $18,200 x 0.623110936 / 0.05 = $224,195.57.
Therefore, the most you should pay for the annuity is $224,195.57.