Steven opened a savings account and deposited $100.00 as principal. The account earns 9% interest, compounded annually. What is the balance after 5 years? Use the formula A = P(1 + (r)/(n))^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent. $____

Question

Steven opened a savings account and deposited $100.00 as principal. The account earns 9% interest, compounded annually. What is the balance after 5 years? Use the formula A = P(1 + (r)/(n))^nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.  Round your answer to the nearest cent. $____

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Identify Variables: Identify the values for the variables in the compound interest formula A = P(1 + (r)/(n))^nt. Here, P = $100 (the principal), r = 9% or 0.09 (the interest rate as a decimal), n = 1 (since the interest is compounded annually), and t = 5 years (the time period).Substitute Values: Substitute the values into the compound interest formula. A = 100(1 + (0.09)/(1))^(1*5)Simplify Expression: Simplify the expression inside the parentheses and then calculate the exponent. A = 100(1 + 0.09)^5 A = 100(1.09)^5Calculate Exponent: Calculate the value of (1.09)^5. (1.09)^5 ≈ 1.53862 (rounded to five decimal places for intermediate calculation)Find Final Balance: Multiply the principal by the result from Step 4 to find the final balance. A = 100 * 1.53862 A ≈ 153.862Round Final Balance: Round the final balance to the nearest cent. A ≈ $153.86

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