Question

If $1,000 is invested at an interest rate of 10% per year, compounded monthly, find the amount of the investment at the end of 4 years

Answer 1

$1489.35

General Formulas and Concepts;

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 Interest Rate Formula:
`\displaystyle A = P(1 + (r)/(n))^(nt)`

• P is principle amount
• r is rate
• n is compounded rate
• t is time (in years)

Explanation:

Step 1: Define

Identify variables

P = 1000

r = 10% = 0.1

n = 12

t = 4

Step 2: Solve for A

1. Substitute in variables [Compounded Interest Rate Formula]:
   `\displaystyle A = 1000(1 + (0.1)/(12))^(12(4))`
2. (Parenthesis) Add:
   `\displaystyle A = 1000((121)/(120))^(12(4))`
3. [Exponents] Multiply:
   `\displaystyle A = 1000((121)/(120))^(48)`
4. Evaluate exponents:
   `\displaystyle A = 1000(1.48935)`
5. Multiply:
   `\displaystyle A = 1489.35`