A person places $3370 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 16 years. Answer:

Question

A person places  $3370 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 16 years. Answer:

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Identify Given Values: Identify the given values from the problem. Principal (P) = $3370 Rate of interest (r) = 9% or 0.09 (as a decimal) Time (t) = 16 years We will use the formula for continuous compounding: V = Pe^(rt)Substitute Values: Substitute the given values into the formula. V = 3370 * e^(0.09 * 16)Calculate Exponent: Calculate the exponent part of the formula. 0.09 * 16 = 1.44Calculate e Value: Calculate e raised to the power of the result from Step 3. e^1.44 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 4. V = 3370 * e^1.44Perform Calculation: Perform the calculation using a calculator to find the value of the investment after 16 years. V ≈ 3370 * 4.220695 V ≈ 14223.53915Round Result: Round the result to the nearest cent. V ≈ $14223.54

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