An investment has been growing at a fixed annual rate of 20% since it was first made; no portion of...

Understanding the Question

We need to find the current value of an investment that has been growing at 20% annually with compound interest, no withdrawals, and all interest reinvested.

What We Need to Determine

To find "How much is the investment now worth?", we need to determine the exact dollar amount. Since the investment grows according to the formula \(\mathrm{Current\ Value} = \mathrm{Initial\ Amount} \times (1.20)^{\mathrm{years}}\), we need either:

• Both the initial investment amount AND the time period, OR
• Some other information that uniquely determines the current value

Key Insight

The question asks for a specific dollar amount, not just a relationship or percentage. This means we need concrete information that pins down the exact value.

Analyzing Statement 1

Statement 1: The value of the investment has increased by 44% since it was first made.

What This Reveals

A 44% increase means the current value is 1.44 times the initial amount. Since growth occurs at 20% per year, let's think about what this means:

• After 1 year: \(1.20 \times\) the initial amount
• After 2 years: \(1.20 \times 1.20 = 1.44 \times\) the initial amount

Perfect! The 44% increase tells us the investment has been growing for exactly 2 years.

What We Still Don't Know

While we now know the investment has been growing for 2 years, we still don't know the initial amount. Whether someone invested $1,000 or $10,000 initially, after 2 years at 20% growth, they'd have 1.44 times their initial investment. Without knowing that starting point, we cannot determine the current value.

[STOP - Not Sufficient!] Statement 1 is NOT sufficient.

This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2: If one year ago $600 had been withdrawn, today the investment would be worth 12% less than it is actually now worth.

The Key Insight

This "what if" scenario creates a unique mathematical constraint. Let's think through what this means:

• In the actual scenario: No withdrawal occurred
• In the hypothetical scenario: $600 was withdrawn one year ago
• The difference: The investment today would be 12% less

The Crucial Connection

Here's the clever part: The 12% difference in today's value must equal exactly what that withdrawn $600 would have grown to in one year at 20% interest.

Step-by-Step Calculation

Let's work through this logically:

1. If $600 had been withdrawn one year ago, it couldn't grow anymore
2. But in reality, that $600 stayed invested and grew at 20% for one year
3. \(\$600 \times 1.20 = \$720\)
4. So the $720 represents the 12% difference mentioned in the statement
5. If $720 = 12% of current value, then:
   • Current value = \(\$720 \div 0.12 = \$6,000\)

We've determined the exact current value!

[STOP - Sufficient!] Statement 2 is sufficient.

This eliminates choices C and E.

The Answer: B

Statement 2 alone provides enough information to determine the exact current value ($6,000), while Statement 1 only tells us how long the investment has been growing but not the actual dollar amount.

Answer Choice B: "Statement 2 alone is sufficient, but Statement 1 alone is not sufficient."