A financial adviser was showing a client the value, rounded to the nearest cent, of an initial investment of $100.00...

Phase 1: Owning the Dataset

Visual Representation - Timeline

Let's create a timeline showing the investment growth:

$100 → $130.01 → ? → ? → ? → ? → ?
Year 0 Year 5 Year 10 Year 15 Year 20 Year 25 Year 30

Key Information

• Initial investment: $100.00
• Value after 5 years: $130.01 (correct)
• Growth rate: constant r% per year
• Two of the remaining values contain transcription errors

Phase 2: Understanding the Question

Finding the Growth Rate

Since the investment grows at a constant rate r% per year:

• $100 × (1 + r)⁵ = $130.01
• (1 + r)⁵ = 1.3001
• 1 + r = 1.3001^(1/5)

Using calculator: 1.3001^(1/5) ≈ 1.0539
So the annual growth rate is approximately 5.39%

What We're Looking For

We need to:

1. Calculate the correct values for years 10, 15, 20, 25, and 30
2. Compare with the given answer choices
3. Identify which two values are incorrect
4. Select the lesser error as "First error" and greater error as "Second error"

Phase 3: Finding the Answer

Calculating Correct Values

Using the compound interest formula with (1 + r)⁵ = 1.3001:

Year 10: $100 × (1 + r)¹⁰ = $100 × (1.3001)² = $100 × 1.69026 ≈ $169.03

Year 15: $100 × (1 + r)¹⁵ = $100 × (1.3001)³ = $100 × 2.19764 ≈ $219.76

Year 20: $100 × (1 + r)²⁰ = $100 × (1.3001)⁴ = $100 × 2.85672 ≈ $285.67

Year 25: $100 × (1 + r)²⁵ = $100 × (1.3001)⁵ = $100 × 3.71288 ≈ $371.29

Year 30: $100 × (1 + r)³⁰ = $100 × (1.3001)⁶ = $100 × 4.82697 ≈ $482.70

Comparing with Given Choices

Let's match our calculated values with the answer choices:

Identifying the Errors

The two transcription errors are:

• $160.02 (should be ~$169.03)
• $317.43 (should be ~$371.29)

Phase 4: Solution

Since we need to select the lesser error as "First error" and the greater error as "Second error":

First error (lesser value): $160.02
Second error (greater value): $317.43