A person places $70500 in an investment account earning an annual rate of 9%, 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 7 years. Answer:

Question

A person places  $70500 in an investment account earning an annual rate of  9%, 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 7 years. Answer:

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Identify Given Values: Identify the given values from the problem. Principal (P) = $70500 Annual interest rate (r) = 9% or 0.09 (as a decimal) Time (t) = 7 years We will use the formula for continuous compounding: V = Pe^(rt)Substitute Values into Formula: Substitute the given values into the formula. V = 70500 * e^(0.09 * 7)Calculate Exponent: Calculate the exponent part of the formula. 0.09 * 7 = 0.63Calculate e Value: Calculate e raised to the power of the result from Step 3. e^0.63 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 4. V = 70500 * e^0.63Perform Calculation: Perform the calculation using a calculator to find the value of the investment after 7 years. V ≈ 70500 * 1.8776 (assuming e^0.63 ≈ 1.8776) V ≈ 132374.28

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