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balandron [24]
3 years ago
7

Hamad invested 5000 AED in an account that pays 5% annual interest.

Mathematics
1 answer:
Andrei [34K]3 years ago
5 0

Answer:

About 33 years.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

Simple Interest Rate Formula: \displaystyle A = P(1 + r)^t

  • <em>P</em> is principle amount
  • <em>r</em> is rate
  • <em>t</em> is time (in years)

Logarithm Property 1: \displaystyle log(a^x) = xloga

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em>P</em> = 5000

<em>r</em> = 5% = 0.05

<em>A</em> = 25000

<em>t</em> = unknown

<u>Step 2: Solve for </u><em><u>t</u></em>

  1. Substitute in variables [Simple Interest Rate Formula]:                                 \displaystyle 25000 = 5000(1 + 0.05)^t
  2. [Division Property of Equality] Divide 5000 on both sides:                          \displaystyle 5 = (1 + 0.05)^t
  3. (Parenthesis) Add:                                                                                            \displaystyle 5 = (1.05)^t
  4. [Equality Property] log both sides:                                                                  \displaystyle log5 = log[(1.05)^t]
  5. Rewrite [Log Property 1]:                                                                                  \displaystyle log5 = tlog1.05
  6. [Division Property of Equality] Isolate <em>t</em>:                                                          \displaystyle \frac{log5}{log1.05}  = t
  7. Rewrite:                                                                                                             \displaystyle t = \frac{log5}{log1.05}
  8. Evaluate:                                                                                                           \displaystyle t = 32.9869
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