Problem

Use the compound interest formula to compute the total amount accumulated and the interest earned. $\$ 8000$ for 4 years at $3.5 \%$ compounded monthly
The total amount accumulated after 4 years is $\$$ (Round to the nearest cent as needed.)

Answer

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Answer

\(\boxed{9200.32}\) is the total amount accumulated after 4 years.

Steps

Step 1 :Given that the principal amount (P) is $8000, the annual interest rate (r) is 3.5%, the number of times that interest is compounded per year (n) is 12, and the time the money is invested for in years (t) is 4.

Step 2 :First, convert the annual interest rate from percentage to decimal form: r = 3.5/100 = 0.035.

Step 3 :Then, substitute these values into the compound interest formula: A = P (1 + r/n)^(nt).

Step 4 :Calculate the total amount accumulated after 4 years: A = 8000 * (1 + 0.035/12)^(12*4) = 9200.315446567025.

Step 5 :Round the total amount to the nearest cent: A = $9200.32.

Step 6 :\(\boxed{9200.32}\) is the total amount accumulated after 4 years.

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