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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.

Respuesta :

Space

Answer:

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: [tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^{nt}[/tex]

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

Step-by-step 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]:             [tex]\displaystyle A = 83927 \bigg( 1 + \frac{0.07}{1} \bigg) ^{1(7)}[/tex]
  2. [Order of Operations] Evaluate parenthesis:                                           [tex]\displaystyle A = 83927(1.07)^{1(7)}[/tex]
  3. [Order of Operations] Simplify exponents:                                             [tex]\displaystyle A = 83927(1.07)^{7}[/tex]
  4. [Order of Operations] Evaluate exponents:                                           [tex]\displaystyle A = 83927(1.60578)[/tex]
  5. [Order of Operations] Multiply:                                                                 [tex]\displaystyle A = 134768.4219764[/tex]
  6. Find difference:                                                                                         [tex]E = 134768.4219764 - 83927[/tex]
  7. [Order of Operations] Subtract:                                                               [tex]E = 50841.4219764[/tex]
  8. Round:                                                                                                       [tex]E \approx 50841[/tex]

∴ 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

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