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An investment of $500 is made at 2.8% nominal yearly interest compounded quarterly. Write an equation that models the amount A the investment is worth t years after the principal has been invested



Answer :

Space

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

Functions

  • Function Notation

Compounded Interest Rate Formula:
[tex]\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg) ^t[/tex]

  • A is final amount
  • P is principle amount
  • r is rate
  • n is compounded rate
  • t is time

Application

Step 1: Define

Let's compile what we know (what we are given).

An investment of $500 means that our principle amount P equals 500.

2.8% nominal yearly interest means that our rate r equals 0.028.

Compounded quarterly means that our compounded rate n equals 4.

So, we have:

[tex]\displaystyle\begin{aligned}P & = 500 \\r & = 0.028 \\n & = 4 \\\end{aligned}[/tex]

Step 2: Work

In order to find an equation that models the final amount A in terms of t years, we can simply substitute in our known variables:

  1. [Compounded Interest Rate Formula] Substitute in variables:
    [tex]\displaystyle A = 500 \bigg( 1 + \frac{0.028}{4} \bigg) ^t[/tex]
  2. [Equation] Simplify:
    [tex]\displaystyle\begin{aligned}A & = 500 \bigg( 1 + \frac{0.028}{4} \bigg) ^t \\A & = 500 (1 + 0.007)^t \\& \boxed{ A = 500(1.007)^t }\end{aligned}[/tex]

Answer

∴ our equation that models the amount A the investment is worth t years after the principle has been invested is:

[tex]\displaystyle \boxed{ A = 500(1.007)^t }[/tex]

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Topic: Algebra I

Unit: Interest Rate Formulas

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