Question

Tiana invests $83,927 in a start-up company. She will be repaid at the end of 7

years at 7% interest compounded annually. Find the amount of interest she will
earn on this investment.
DO NOT ROUND ANY NUMBERS UNTIL YOUR FINAL ANSWER!
Round to the nearest dollar.

Answer 1

Tiana will earn approximately $50,841 with her investment amount total to be $134,768.

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 II

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

• P is principal amount
• r is rate
• n is compound rate
• t is time

Explanation:

Step 1: Define

Identify variables.

P = $83,927

r = 0.07

n = 1

t = 7

Step 2: Find Return Investment

1. Substitute in variables [Compounded Interest Rate Formula]:
   `\displaystyle A = 83927 \bigg( 1 + (0.07)/(1) \bigg) ^(1(7))`
2. [Order of Operations] Evaluate parenthesis:
   `\displaystyle A = 83927(1.07)^(1(7))`
3. [Order of Operations] Simplify exponents:
   `\displaystyle A = 83927(1.07)^(7)`
4. [Order of Operations] Evaluate exponents:
   `\displaystyle A = 83927(1.60578)`
5. [Order of Operations] Multiply:
   `\displaystyle A = 134768.4219764`
6. Find difference:
   `E = 134768.4219764 - 83927`
7. [Order of Operations] Subtract:
   `E = 50841.4219764`
8. Round:
   `E \approx 50841`

∴ After Tiana invests $83,927 with a 7% interest compounded annually in a timeframe of 7 years, she would make $50,841 with a total account value of $134,768.

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Topic: Algebra II