Question

Solve the problem.

An initial investment of $930 is appreciated for 19 years in an account that earns
6% interest, compounded continuously. Find the amount of money in the
account at the end of the period.
$1275.35
$22,067.28
$12,424,545.93
$2907.89

Answer 1

$2907.89

General Formulas and Concepts:

Symbols

• e (Euler's number) ≈ 2.71828

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

Compounded Continuously Formula:
`\displaystyle A = Pe^(rt)`

• P is principle amount
• r is rate
• t is time

Explanation:

Step 1: Define

Identify variables

P = 930

t = 19

r = 6% = 0.06

Step 2: Find Interest

1. Substitute in variables [Compounded Continuously Formula]:
   `\displaystyle A = 930e^(19 \cdot 0.06)`
2. [Exponents] Multiply:
   `\displaystyle A = 930e^(1.14)`
3. Evaluate exponents:
   `\displaystyle A = 930(3.12677)`
4. Multiply:
   `\displaystyle A = 2907.89`