27.03.2023 - 18:34

You want to have $2 million when you retire in 40 years. If you can earn 12% per year, how much do you need to deposit on a monthly basis if the first payment is made in one month?

Question:

You want to have $2 million when you retire in 40 years. If you can earn 12% per year, how much do you need to deposit on a monthly basis if the first payment is made in one month?

Answers (1)
  • Fyutch
    April 3, 2023 в 14:21

    To calculate the monthly deposit required, we need to use the present value of an annuity formula. The present value of an annuity formula calculates the present value of a series of equal payments to be made at regular intervals, such as monthly.

    Given that we want to have $2 million in 40 years and we can earn 12% per year, we need to calculate the present value of the annuity that would provide that amount at retirement.

    Using the present value of an annuity formula:

    PV = PMT x [(1 - (1 + r)^(-n)) / r]

    where: PV = present value of the annuity PMT = monthly payment r = interest rate per period (monthly in this case) n = total number of periods (40 x 12 = 480 months)

    Plugging in the values we have:

    PV = PMT x [(1 - (1 + 0.12/12)^(-480)) / (0.12/12)] PV = PMT x [(1 - (1.01)^(-480)) / (0.01)]

    We want the present value to be $2 million, so:

    $2,000,000 = PMT x [(1 - (1.01)^(-480)) / (0.01)]

    Solving for PMT:

    PMT = $2,000,000 / [(1 - (1.01)^(-480)) / (0.01)] PMT = $2,000,000 / 41.6824 PMT = $47,964.16

    Therefore, to have $2 million when you retire in 40 years, you would need to deposit \approx imately $47,964.16 per month, starting from one month from now, and earning a 12% annual interest rate.

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