Questions: If 10,000 is invested at 6% interest compounded monthly, find the interest earned in 17 years. The interest earned in 17 years is . (Do not round until the final answer. Then round to two decimal places as needed.)

If 10,000 is invested at 6% interest compounded monthly, find the interest earned in 17 years.

The interest earned in 17 years is . (Do not round until the final answer. Then round to two decimal places as needed.)
Transcript text: If $\$ 10,000$ is invested at $6 \%$ interest compounded monthly, find the interest earned in 17 years. The interest earned in 17 years is \$ $\square$ . (Do not round until the final answer. Then round to two decimal places as needed.)
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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 from a percentage to a decimal, divide by 100: \(r = \frac{6}{100} = 0.06\).

Step 2: Calculate the compound interest

Using the formula \(A = P(1 + \frac{r}{n})^{nt}\), where \(P = 10000\), \(r = 0.06\), \(n = 12\), and \(t = 17\), we calculate the accumulated amount. \(A = 10000(1 + \frac{0.06}{12})^{12*17} = 27661.556\).

Step 3: Calculate the interest earned

The interest earned is calculated by subtracting the principal from the accumulated amount: \(Interest = A - P = 27661.556 - 10000 = 17661.556\).

Step 4: Round the final answer

Rounding the interest earned to 2 decimal places gives: \(Interest = 17661.56\).

Final Answer

The interest earned on the investment, rounded to 2 decimal places, is \(\$17661.56\).

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