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Valerie deposits $1,900 in an account that
earns 3% interest, compounded quarterly.
How much is in the account after six years?

Sagot :

Space

Answer:

$2273.19

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

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

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

Step-by-step explanation:

Step 1: Identify Variables

P = $1900

r = 3% = 0.03

n = 4

Step 2: Solve for A

  1. Substitute [CIRF]:                    [tex]\displaystyle A = 1900(1 + \frac{0.03}{4})^{4(6)}[/tex]
  2. (Parenthesis) Divide:              [tex]\displaystyle A = 1900(1 + 0.0075)^{4(6)}[/tex]
  3. (Parenthesis) Add:                  [tex]\displaystyle A = 1900(1.0075)^{4(6)}[/tex]
  4. (Exponents) Multiply:             [tex]\displaystyle A = 1900(1.0075)^{24}[/tex]
  5. Exponents:                             [tex]\displaystyle A = 1900(1.19641)[/tex]
  6. Multiply:                                  [tex]\displaystyle A = 2273.19[/tex]
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