Question

Sandy invest $1500 into an account with 3. 5% interest, compounded quarterly. How much money will be in the account after 8 years? Be sure to not round until the very end and then round to the nearest cent. I​

Answer 1

Sandy will have $1982.28 in her bank account.

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 \bigg( 1 + (r)/(n) \bigg)^(nt)`

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

Explanation:

Step 1: Define

Identify variables.

P = $1500

r = 0.035

n = 4

t = 8

Step 2: Find Accumulative Money

1. Substitute in variables [Compounded Interest Rate Formula]:
   `\displaystyle A = 1500 \bigg( 1 + (0.035)/(4) \bigg)^(4(8))`
2. [Exponents] Multiply:
   `\displaystyle A = 1500 \bigg( 1 + (0.035)/(4) \bigg)^(32)`
3. (Parenthesis) Simplify:
   `\displaystyle A = 1500(1.00875)^(32)`
4. [Order of Operations] Evaluate:
   `\displaystyle A = 1982.28`

∴ Sandy will have a final account balance of $1,982.28 after her initial deposit of $1,500 in the timeframe of 8 years.

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Topic: Algebra I