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Jessica wants to accumulate $11,000 by the end of 4 years in a special bank account, which she had opened for this purpose. To achieve this goal, Jessica plans to deposit a fixed sum of money into the account at the end of the month over the 4-year period. If the bank pays interest at the rate of 6% per year compounded monthly, how much does she have to deposit each month into her account? (Round your answer to the nearest cent.)

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Answer:

Ans. Jessica has to make monthly deposits of $203.34 in order to get $11,000 at the end of the fourth year, at a rate of 6% compounded monthly.

Step-by-step explanation:

Hi, the first thing to do is to convert that compounded rate into an effective rate, that is by just dividing by 12, therefore, 0.06/12=0.005 or 0.5% effective monthly.

We also know that this deposits are going to take place at the end of every month, for 4 years, that means 48 months.

And to find the value of the monthly deposit, we need to use the following equation and solve for A

[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r}[/tex]

Filling it up, we get:

[tex]11,000=\frac{A((1+0.005)^{48}-1) }{0.005}[/tex]

[tex]11,000=\frac{A((0,270489161) }{0.005}[/tex]

[tex]11,000=A( 54,098 )[/tex]

[tex]A=203.34[/tex]

Best of luck

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