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

Answer:

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: $\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg)^{nt}$

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

Step-by-step 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]:                 $\displaystyle A = 1500 \bigg( 1 + \frac{0.035}{4} \bigg)^{4(8)}$
2. [Exponents] Multiply:                                                                                    $\displaystyle A = 1500 \bigg( 1 + \frac{0.035}{4} \bigg)^{32}$
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