Questions: Find the final amount of money in an account if 8,200 is deposited at 7% interest compounded weekly and the money is left for 5 years. The final amount is Round answer to 2 decimal places

Find the final amount of money in an account if 8,200 is deposited at 7% interest compounded weekly and the money is left for 5 years. The final amount is Round answer to 2 decimal places

Solution

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Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, we divide the rate by 100. Thus, \(r = 7 / 100 = 0.07\).

Step 2: Identify the number of times the interest is compounded per year

The interest is compounded \(n = 52\) times per year.

Step 3: Determine the time period in years for which the money will be left in the account

The money will be left in the account for \(t = 5\) years.

Step 4: Substitute the values into the compound interest formula

Substituting the values into the formula, we get \(A = 8200(1 + \frac{0.07}{52})^{52*5} = 11633.615\).

Step 5: Calculate the final amount after the specified time period

The final amount after rounding to 2 decimal places is \(A = 11633.62\).

Final Answer:

The final amount in the account after 5 years is $11633.62.

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