A person places $427 in an investment account earning an annual rate of 3.7%, 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  $427 in an investment account earning an annual rate of  3.7%, 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:

Bytelearn · Accepted Answer

Identify Given Values: Identify the given values from the problem. Principal (P) = $427 Rate of interest (r) = 3.7% or 0.037 (as a decimal) Time (t) = 16 years We will use the formula for continuous compounding: V = Pe^(rt)Substitute into Formula: Substitute the given values into the formula. V = 427 * e^(0.037 * 16)Calculate Exponent: Calculate the exponent part of the formula. 0.037 * 16 = 0.592Calculate e Value: Calculate e raised to the power of the result from Step 3. e^0.592 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 4. Assuming e^0.592 ≈ 1.808 (using a calculator) V = 427 * 1.808Perform Multiplication: Perform the multiplication to find the final value. V ≈ 427 * 1.808 ≈ 772.216Round Final Value: Round the final value to the nearest cent. V ≈ $772.22

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