Question

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $5000 per month. You have access to an account that pays an APR of 8.4% compounded monthly. This requires a nest egg of $626,174.58.

What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)

Answer 1

To achieve the desired monthly yield at retirement, a monthly deposit of approximately $615.27 is required.

Step-by-step explanation:

Step 1:

Convert the desired monthly income to an annual income:

$5000/month * 12 months = $60,000/year

Step 2:

Find the future value of the retirement annuity using the given APR and number of years:

Nest egg = $626,174.58

Step 3:

Calculate the monthly deposit required to achieve the desired monthly yield at retirement using the future value formula:

Future value = Monthly deposit * [ ((1 + (APR/12))^n - 1) / (APR/12) ]

Where n = number of months (25 years * 12 months/year)

Substituting the known values:

$626,174.58 = Monthly deposit * [ ((1 + (0.084/12))^(25*12) - 1) / (0.084/12) ]

Solving for Monthly deposit:

Monthly deposit = $626,174.58 / [ ((1 + (0.084/12))^(25*12) - 1) / (0.084/12) ]

Using this formula, the monthly deposit required to achieve the desired monthly yield at retirement is approximately $615.27