A person places $118 in an investment account earning an annual rate of 3.3%, compounded continuously. Using the formula V=Pe^(rt), where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 9 years. Answer:

Question

A person places  $118 in an investment account earning an annual rate of  3.3%, compounded continuously. Using the formula  V=Pe^(rt), where  V is the value of the account in  t years,  P is the principal initially invested,  e is the base of a natural logarithm, and  r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 9 years. Answer:

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Identify Given Values: Identify the given values from the problem. Principal (P) = $118 Rate of interest (r) = 3.3% or 0.033 (since 1% = 0.01) Time (t) = 9 years We will use the formula for continuous compounding: V = Pe^(rt)Convert Percentage to Decimal: Convert the percentage rate to a decimal. 3.3% = 3.3/100 = 0.033 This is the value of r that we will use in the formula.Substitute Values into Formula: Substitute the values into the formula. V = 118 * e^(0.033 * 9)Calculate Exponent: Calculate the exponent part of the formula. 0.033 * 9 = 0.297Calculate e Value: Calculate e raised to the power of the result from Step 4. e^0.297 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 5. Assuming e^0.297 ≈ 1.34591 (using a calculator) V = 118 * 1.34591Perform Multiplication: Perform the multiplication to find the final value. V ≈ 118 * 1.34591 ≈ 158.81738Round Final Value: Round the final value to the nearest cent. V ≈ $158.82

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