Exact Calculation: How 150 × (1.08)² Equalto 175 (Approximately)

When tackling exponential growth problems, precise calculations are essential—especially in finance, investing, and compound interest. One such calculation is solving 150 × (1.08)² = ? and understanding why the result approximates to 175. In this SEO-optimized article, we break down the exact mathematical process, explain the importance of rounding, and explore real-world applications where such a computation matters.

Understanding the Context

Understanding the Formula: 150 × (1.08)²

At its core, the expression 150 × (1.08)² represents compound growth. Here’s what each part means:

  • 150 is the initial value or principal amount.
  • (1.08)² represents a growth factor raised to the power of 2, simulating a 8% annual increase compounded over two years.
  • The expression models how an investment or balance grows when increasing by 8% each year.

Let’s break it down step-by-step:

Exact: 150 × (1.08)^2 = 150 × 1.1664 = 174.96 ≈ 175

Key Insights

Step 1: Compute (1.08)²

Exponentiation means multiplying the base by itself:
(1.08)² = 1.08 × 1.08 = 1.1664

This value shows 8% growth compounded once over two years.

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So \( f(x) = rac{(2x - 1)(x - 1)}{x - 1} = 2x - 1 \) for \( x
Removing discontinuity, \( f(1) = 2(1) - 1 = 1 \).
A sequence is defined recursively by \( a_1 = 2 \), \( a_{2} = 3 \), and \( a_{n} = a_{n-1} + 2a_{n-2} \) for \( n \ge 3 \). Find \( a_6 \).

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Final Thoughts

Step 2: Multiply by Initial Amount (150)

Next, multiply the base amount by the growth factor:
150 × 1.1664 = 174.96

This exact value confirms that 8% annual growth over two years on $150 yields $174.96.

Step 3: Round to Approximate Value — Why 175?

In everyday contexts like finance or reporting, exact figures like 174.96 are often rounded to make data simpler and more digestible. Rounding 174.96 to 175 is common practice, especially when:

  • Presenting financial results for clarity
  • Discussing rough estimates in growth projections
  • Avoiding overcomplication with decimal precision

Thus, 150 × (1.08)² ≈ 175 when rounded to the nearest dollar.

Real-World Application: Compound Interest and Investment Growth