Question

Hamad invested 5000 AED in an account that pays 5% annual interest.
After how many years will the value in Hamad's account be $25,000? ​

Answer 1

Answer:

About 33 years.

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  

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

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

• P is principle amount
• r is rate
• t is time (in years)

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

Step-by-step explanation:

Step 1: Define

Identify

P = 5000

r = 5% = 0.05

A = 25000

t = unknown

Step 2: Solve for t

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 t:                                                          $\displaystyle \frac{log5}{log1.05} = t$
7. Rewrite:                                                                                                             $\displaystyle t = \frac{log5}{log1.05}$
8. Evaluate:                                                                                                           $\displaystyle t = 32.9869$