23.03.2023 - 21:36

You have just retired with savings of $1.5 million. If you expect to live for 25 years and to earn 9% per year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.

You have just retired with savings of $1.5 million. If you expect to live for 25 years and to earn 9% per year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.

Answers (1)
  • chuhol
    April 6, 2023 в 17:28

    Assuming that you want your savings to last for 25 years, and you earn a return of 9% per year, you can use the formula for the present value of an annuity to calculate the amount you can afford to spend each year. The present value of an annuity formula is:

    PV = (PMT / r) * (1 - (1 + r)^-n)

    where PV is the present value of the annuity, PMT is the amount of each payment, r is the interest rate per period, and n is the number of periods.

    In this case, PMT is the amount you can afford to spend each year, r is 9% per year, and n is 25 years. We can rearrange the formula to solve for PMT:

    PMT = PV * r / (1 - (1 + r)^-n)

    Substituting the values given, we get:

    PMT = $1.5 million * 9% / (1 - (1 + 9%)^-25)

    PMT = $1.5 million * 0.09 / (1 - 0.2118)

    PMT = $1.5 million * 0.09 / 0.7882

    PMT = $134,235.08

    Therefore, you can afford to spend \approx imately $134,235.08 each year if you want your savings to last for 25 years, assuming an annual return of 9%. It's important to note that this calculation assumes that you will spend the same amount each year and that inflation is not taken into account.

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