Question

When his aunt​ died, Ariel inherited an annuity paying ​$5500 every quarter into a savings account for six years. The terms of the will state that he cannot withdraw any money for the first ​six years, and then he can withdraw equal amounts at the end of each quarter for five years. If interest is ​5.63% compounded quarterly ​, what will be the size of each​ withdrawal?

Answer 1

To find the size of each withdrawal, we need to calculate the present value of the annuity. First, let's calculate the future value of the annuity after 6 years. Then, we can find the present value of the future value to determine the size of each withdrawal.

Step-by-step explanation:

To find the size of each withdrawal, we need to calculate the present value of the annuity. First, let's calculate the future value of the annuity after 6 years. Since the annuity pays $5500 every quarter for 6 years, there will be a total of 24 payments. Using the formula for future value of an annuity, the future value will be:

$5500 * ((1 + 0.0563/4)^(4*6) - 1) / (0.0563/4)

Now, let's find the present value of the future value we just calculated. We can use the formula for present value of a lump sum, where the future value is $5500 * ((1 + 0.0563/4)^(4*6) - 1) / (0.0563/4) and the time period is 5 years. Solving for the present value, we get the size of each withdrawal to be $5500 * ((1 + 0.0563/4)^(4*6) - 1) / (0.0563/4) / ((1 + 0.0563/4)^(4*5) - 1) = $amount.