Question

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.

Answer 1

`\displaystyle V \approx 25129.99`

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:
`\displaystyle V = Pe^(rt)`

• 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

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]:
   `\displaystyle V = 9680e^(0.053(18))`
2. Multiply exponents:
   `\displaystyle V = 9680e^(0.954)`
3. Evaluate exponents:
   `\displaystyle V = 9680(2.59607)`
4. Multiply:
   `\displaystyle V = 25129.988684793`
5. Round:
   `\displaystyle V \approx 25129.99`