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A fund of ​$30 comma 000 has been set up to pay for​ Edwin's music lessons over the next twelve years. If interest is​ 6.21% compounded​ monthly, what is the size of each​ month-end withdrawal from the​ fund?
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Part 1
The amount of each​ month-end withdrawal is ​$
  
enter your response here.
​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)



Answer :

sqdancefan

Answer:

  296.03 dollars

Step-by-step explanation:

You want the amount of each month-end withdrawal that can be made for 12 years from a fund of 30,000 dollars earning 6.21% interest compounded monthly.

Amortization

The amortization formula can be used to find the amount of the payment that can be withdrawn monthly for n months when the monthly interest rate is r.

  [tex]A=\dfrac{Pr}{1-(1+r)^{-n}}\\\\\\A=\dfrac{30\,000\cdot0.005175}{1-1.005175^{-144}}\approx296.0257[/tex]

The dollar amount of each month-end withdrawal is 296.03.

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Additional comment

Since we have rounded up the withdrawal amount, the last withdrawal will be a few cents short.

In 12 years, there are 12·12 = 144 months. The monthly interest rate as a decimal is 6.21%/12 = 0.005175.

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