A person places $6520 in an investment account earning an annual rate of 7.7%, 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 14 years. Answer:

Question

A person places  $6520 in an investment account earning an annual rate of  7.7%, 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 14 years. Answer:

Bytelearn · Accepted Answer

Identify Values: Identify the given values from the problem. Principal (P) = $6520 Rate of interest (r) = 7.7% or 0.077 (as a decimal) Time (t) = 14 years We will use the formula for continuous compounding: V = Pe^(rt)Convert Rate to Decimal: Convert the percentage rate to a decimal by dividing by 100. r = 7.7% = 7.7/100 = 0.077Substitute into Formula: Substitute the values into the formula. V = 6520 * e^(0.077 * 14)Calculate Exponent: Calculate the exponent part of the formula. 0.077 * 14 = 1.078Calculate e^Result: Calculate e raised to the power of the result from Step 4. e^1.078 (Use a calculator for this step)Multiply by Principal: Multiply the principal by the result from Step 5. V = 6520 * e^1.078 (Using a calculator, e^1.078 ≈ 2.940) V ≈ 6520 * 2.940Perform Final Multiplication: Perform the multiplication to find the final value. V ≈ 6520 * 2.940 ≈ 19168.80

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