A person places $634 in an investment account earning an annual rate of 6.4%, 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 13 years. Answer:

Question

A person places  $634 in an investment account earning an annual rate of  6.4%, 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 13 years. Answer:

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Identify Given Values: Identify the given values from the problem. Principal (P) = $634 Rate of interest (r) = 6.4% or 0.064 (as a decimal) Time (t) = 13 years We will use the formula V = Pe^(rt) to find the value of the account after 13 years.Convert Rate to Decimal: Convert the percentage rate to a decimal. To convert a percentage to a decimal, divide by 100. r = 6.4% = 6.4/100 = 0.064Substitute Values: Substitute the values into the formula. V = 634 * e^(0.064 * 13)Calculate Exponent: Calculate the exponent part of the formula. 0.064 * 13 = 0.832Calculate e^Exponent: Calculate e raised to the power of the exponent. e^0.832 (This calculation requires a scientific calculator or software that can compute e to a given power.)Multiply Principal: Multiply the principal by the result from Step 5. Assuming e^0.832 ≈ 2.2996 (using a calculator) V = 634 * 2.2996Perform Multiplication: Perform the multiplication to find the final value. V ≈ 634 * 2.2996 ≈ 1457.9984Round Final Value: Round the final value to the nearest cent. V ≈ $1457.9984 ≈ $1458.00

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