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Sarah invests her graduation money of $1,750 in an annuity that pays an interest rate of 6% compounded annually. Sarah wants to determine the amount of money that will be in the account after a certain number of years if she leaves the money in the account and doesn’t make any deposits or withdrawals. Which function can Sarah use to describe her investment growth?

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Answer:

[tex]A = 1750(1.06)^{t}[/tex]

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

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

Step-by-step explanation:

Step 1: Define

Given

Principle Amount = $1750

r = 6% = 0.06

n = 1 (compounded annually)

Step 2: Write function

Substitute into formula

  1. Substitute [CIR]:                    [tex]A = 1750(1 + \frac{0.06}{1} )^{1t}[/tex]
  2. (Parenthesis) Divide:            [tex]A = 1750(1 + 0.06)^{1t}[/tex]
  3. (Exponents) Multiply:           [tex]A = 1750(1 + 0.06)^{t}[/tex]
  4. (Parenthesis) Add:               [tex]A = 1750(1.06)^{t}[/tex]

This equation tells us how much money A the investment has gained over t years.