A person places $78800 in an investment account earning an annual rate of 7.4%, 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 3 years. Answer:

Question

A person places  $78800 in an investment account earning an annual rate of  7.4%, 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 3 years. Answer:

Bytelearn · Accepted Answer

Identify Given Values: Identify the given values from the problem. Principal (P) = $78800 Rate of interest (r) = 7.4% or 0.074 (as a decimal) Time (t) = 3 years We will use the formula V = Pe^(rt) to find the value of the account after 3 years.Convert Percentage to Decimal: Convert the percentage rate to a decimal. 7.4% as a decimal is 0.074.Substitute Values into Formula: Substitute the given values into the formula. V = 78800 * e^(0.074 * 3)Calculate Exponent: Calculate the exponent part of the formula. 0.074 * 3 = 0.222Calculate e Value: Calculate e raised to the power of the result from Step 4. e^0.222 (Use a calculator for this step)Multiply Principal: Multiply the principal by the result from Step 5. V = 78800 * e^0.222 (Use a calculator to find the value of e^0.222 and then multiply by 78800)Round Final Result: Round the final result to the nearest cent. (Use a calculator to get the final value and round it to two decimal places)

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