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Math

QuestionYou have \$400,000 saved at 4\% interest. How much can you withdraw monthly for 20 years?

Studdy Solution

STEP 1

Assumptions1. The initial retirement savings is $400,000. The interest rate is4%
3. The time for withdrawal is20 years4. The interest is compounded monthly5. The withdrawal amount is the same each month

STEP 2

First, we need to find the monthly interest rate. We can do this by dividing the annual interest rate by12.
Monthly interest rate=Annual interest rate/12Monthly\, interest\, rate = Annual\, interest\, rate /12

STEP 3

Now, plug in the given values for the annual interest rate to calculate the monthly interest rate.
Monthly interest rate=%/12Monthly\, interest\, rate =\% /12

STEP 4

Convert the percentage to a decimal value.
4%=0.044\% =0.04Monthly interest rate=0.04/12Monthly\, interest\, rate =0.04 /12

STEP 5

Calculate the monthly interest rate.
Monthly interest rate=0.04/12=0.00333Monthly\, interest\, rate =0.04 /12 =0.00333

STEP 6

Next, we need to find the total number of months for withdrawal. We can do this by multiplying the number of years by12.
Total number of months=Number of yearstimes12Total\, number\, of\, months = Number\, of\, years \\times12

STEP 7

Plug in the given values for the number of years to calculate the total number of months.
Total number of months=20times12Total\, number\, of\, months =20 \\times12

STEP 8

Calculate the total number of months.
Total number of months=20times12=240Total\, number\, of\, months =20 \\times12 =240

STEP 9

We can now calculate the monthly withdrawal amount using the formula for the annuity payment, which is given byMonthly withdrawal=Initial savingstimesMonthly interest rate−(+Monthly interest rate)−Total number of monthsMonthly\, withdrawal = Initial\, savings \\times \frac{Monthly\, interest\, rate}{ - ( + Monthly\, interest\, rate)^{-Total\, number\, of\, months}}

STEP 10

Plug in the values for the initial savings, monthly interest rate, and total number of months to calculate the monthly withdrawal.
Monthly withdrawal=$400,000times0.00333−(+0.00333)−240Monthly\, withdrawal = \$400,000 \\times \frac{0.00333}{ - ( +0.00333)^{-240}}

STEP 11

Calculate the monthly withdrawal amount.
Monthly withdrawal=$400,000times0.00333−(+0.00333)−240=$,423.71Monthly\, withdrawal = \$400,000 \\times \frac{0.00333}{ - ( +0.00333)^{-240}} = \$,423.71You will be able to withdraw approximately $,423.71 each month.

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