A person places $73100 in an investment account earning an annual rate of 7.1%, 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 6 years. Answer:

Question

A person places  $73100 in an investment account earning an annual rate of  7.1%, 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 6 years. Answer:

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Identify Given Values: Identify the given values from the problem. Principal (P) = $73100 Rate of interest (r) = 7.1% or 0.071 (as a decimal) Time (t) = 6 years We will use the formula for continuous compounding: V = Pe^(rt)Convert Percentage to Decimal: Convert the percentage rate to a decimal. 7.1% = 0.071 This is necessary to use in the formula.Substitute Values into Formula: Substitute the given values into the formula. V = 73100 * e^(0.071 * 6)Calculate Exponent: Calculate the exponent part of the formula. 0.071 * 6 = 0.426Calculate e^Result: Calculate e raised to the power of the result from Step 4. e^0.426 (Use a calculator for this step)Multiply Principal by Result: Multiply the principal by the result from Step 5. V = 73100 * e^0.426 (Use a calculator for this step)Calculate Final Value: Calculate the final value to the nearest cent. V ≈ 73100 * 1.531446 (assuming e^0.426 ≈ 1.531446) V ≈ 111900.566 Round to the nearest cent. V ≈ $111900.57

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