Question

Earned.

James was 65 and ready for retirement. He had $700,000 in his retirement savings and wanted
to invest it in an annuity earning 6% annually. He decided he would set the payments to payout
over 40 years to assure his money would not run out. How much would James receive as his
annual income from his annuity? $

Answer 1

$22,649.92

Explanation:

To calculate James' annual income from his annuity, we can use the formula for the future value of an ordinary annuity:

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

Where:

FV is the future value (the total amount James will receive over 40 years)

P is the annual payment (the amount James will receive each year)

r is the interest rate per period (6% annually, which is 0.06)

n is the number of periods (40 years)

We need to solve for P, the annual payment.

Given:

FV = $700,000

r = 0.06

n = 40

$700,000 = P * [(1 + 0.06)^40 - 1] / 0.06

To simplify the equation, let's calculate [(1 + 0.06)^40 - 1] / 0.06:

[(1 + 0.06)^40 - 1] / 0.06 ≈ 30.8645

Now, we can solve for P:

$700,000 = P * 30.8645

Divide both sides of the equation by 30.8645:

P ≈ $700,000 / 30.8645

P ≈ $22,649.92

Therefore, James would receive approximately $22,649.92 as his annual income from his annuity.