A = 5000 à (1,02)^12 â 5000 à 1,26824 = 6341,20 - Portal da Acústica
Simplified Calculation: A = 5000 × (1.02)^12 Wonderfully Prepares You for a 634.12 Gain
Simplified Calculation: A = 5000 × (1.02)^12 Wonderfully Prepares You for a 634.12 Gain
Understanding Compound Growth: A = 5000 × (1.02)^12 Explained
When managing investments, savings, or long-term financial growth, understanding compound interest is essential. One classic example involves calculating future value using a growth factor and a principal amount. In this article, we break down the formula A = 5000 × (1.02)^12, demonstrating how a modest 2% annual growth over 12 years transforms $5000 into $6341.20 — a perfect case study in the power of compounding.
Understanding the Context
Breaking Down the Formula: A = 5000 × (1.02)^12
At first glance, the equation may appear straightforward, but each component tells a meaningful story about financial growth:
- A represents the future value after 12 years.
- 5000 is the initial principal amount — your starting investment or savings.
- 1.02 is the annual growth factor, representing a 2% increase per year (since 1 + 0.02 = 1.02).
- (1.02)^12 calculates the compounded growth over 12 full years.
Key Insights
Let’s see step by step how this becomes $6341.20.
Step-by-step Calculation: (1.02)^12 = ?
Calculating powers may sound complex, but (1.02)^12 simplifies neatly:
Using logarithms or a calculator, we find:
(1.02)^12 ≈ 1.26824
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Final Calculation: Putting It All Together
Now plug the growth factor into the formula:
A = 5000 × 1.26824 = 6341.20
This means a $5000 investment growing at 2% per year for 12 years results in $6341.20 — highlighting the compounding effect of consistent growth.
Why This Matters: Real-World Implications
This formula is widely applicable — whether tracking retirement savings, investment portfolios, or recurring savings plans. Even a modest annual return of 2% compounds significantly over time:
| Time (Years) | Value |
|--------------|-----------------|
| 1 | $5100.00 |
| 5 | ≈$5612.56 |
| 10 | ≈$6105.10 |
| 12 | $6341.20 |
Small percentage increases, compounded systematically, build substantial wealth over years.
