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

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`

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 (log5)/(log1.05) = t`
7. Rewrite:
   `\displaystyle t = (log5)/(log1.05)`
8. Evaluate:
   `\displaystyle t = 32.9869`