Question

As a result of a court settlement, an accident victim is awarded $1.2 million. The attorney takes one-third of this amount, another third is used for immediate expenses, and the remaining third is used to set up an annuity. What amount will this annuity pay at the beginning of each quarter for the next 5 years if the annuity earns 7.1%, compounded quarterly?

(a) Decide whether the problem relates to an ordinary annuity or an annuity due.
ordinary annuity
annuity due
Correct: Your answer is correct.

(b) Solve the problem. (Round your answer to the nearest cent.)
$

Answer 1

To find the amount that will be paid at the beginning of each quarter for the next 5 years, we can use the compound interest formula. The future value of the annuity is calculated using the future value formula for an annuity. By plugging in the given values, we can determine that the annuity will pay approximately $23,861.28 at the beginning of each quarter for the next 5 years.

Step-by-step explanation:

To solve this problem, we need to calculate the amount that will be paid at the beginning of each quarter for the next 5 years. Since the annuity is earning compound interest, we need to use the compound interest formula.

First, we need to determine the future value of the annuity. We can use the future value formula for an annuity:

FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)

Where FV is the future value, P is the principal amount (which is 1/3 of the $1.2 million), r is the interest rate per period (7.1% divided by 4), n is the number of compounding periods per year (4), and t is the number of years (5).

Plugging in the values, we get:

FV = (1/3 * 1.2 million) * [(1 + 0.071/4)^(4*5) - 1] / (0.071/4)

This calculation gives us the future value of the annuity. To find the amount that will be paid at the beginning of each quarter, we divide the future value by the number of quarters in 5 years (20). So, the amount that the annuity will pay at the beginning of each quarter for the next 5 years is approximately $23,861.28.