For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent annually and $400 a month in a bond account earn

Question

For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent annually and $400 a month in a bond account earning 4 percent per year. When you retire in 20 years, you will combine your money into an account with a return of 10 percent per year. How much can you withdraw each month during retirement assuming a 30-year withdrawal period?

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Calantha 2 months 2021-07-22T13:42:10+00:00 1 Answers 4 views 0

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    2021-07-22T13:44:07+00:00

    Answer:

    Monthly withdraw= $204.55

    Step-by-step explanation:

    First, we need to calculate the value of the account at the moment of retirement using the following formula:

    FV= {A*[(1+i)^n-1]}/i

    A= monthly deposit

    Stock:

    Monthly deposit= $600

    Interest rate= 0.07/12= 0.00583

    Number of periods (n)= 20*12= 240 months

    FV= {600*[(1.00583^240) – 1]} / 0.00583

    FV= $312,404.24

    Bond:

    Monthly deposit= $400

    Interest rate= 0.04/12= 0.0033

    Number of periods (n)= 20*12= 240 months

    FV= {400*[(1.0033^240) – 1]} / 0.0033

    FV= $146,052.20

    Total value at retirement= $458,456.44

    Now, we can determine the monthly withdrawals after retirement:

    Monthly withdraw= (FV*i) / [1 – (1+i)^(-n)]

    FV= 458,456.44

    n= 30*12= 360

    i= 0.1/12= 0.0083

    Monthly withdraw= (458,456.44*0.0083) / [(1.0083^360) – 1]

    Monthly withdraw= $204.55

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