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A person places $9680 in an investment account earning an annual rate of 5.3%, compounded continuously. Using the formula V = P e r t 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 18 years.

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Answer:

[tex]\displaystyle V \approx 25129.99[/tex]

General Formulas and Concepts:

Math

  • Euler's number e ≈ 2.718

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

Continuously Compounded Interest Rate Formula: [tex]\displaystyle V = Pe^{rt}[/tex]

  • V is value of account
  • P is principle initially invested
  • e is base of ln
  • r is rate of interest
  • t is time in years

Step-by-step explanation:

Step 1: Define

P = $9680

r = 5.3% = 0.053

t = 18 years

Step 2: Solve

  1. Substitute in variables [Continuously Compounded Interest Rate]:            [tex]\displaystyle V = 9680e^{0.053(18)}[/tex]
  2. Multiply exponents:                                                                                        [tex]\displaystyle V = 9680e^{0.954}[/tex]
  3. Evaluate exponents:                                                                                       [tex]\displaystyle V = 9680(2.59607)[/tex]
  4. Multiply:                                                                                                           [tex]\displaystyle V = 25129.988684793[/tex]
  5. Round:                                                                                                             [tex]\displaystyle V \approx 25129.99[/tex]

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