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Here, we're dealing with two different types of interest calculations in one question. Let's walk through this together so you can see exactly what's happening with Kevin's money.
Here's how to approach this:
Understanding the Setup
Kevin made two separate investments:
The key thing you need to recognize is that these require different calculation approaches - one is simple interest, the other is compound interest.
Step 1: Calculate Simple Interest (First Investment)
For simple interest, you just calculate a percentage of the original amount. Nothing more, nothing less.
Kevin invested $8,000 at 6% for 1 year.
Interest = \(0.06 \times 8,000 = 480\)
So Kevin earned $480 from his first investment.
Step 2: Calculate Compound Interest (Second Investment)
Now here's where it gets interesting. "Compounded semiannually" means the interest is calculated and added to the account twice per year - every 6 months.
Since the annual rate is 8%, each 6-month period earns 4% interest (because 8% ÷ 2 = 4%).
Let me show you what happens step by step:
After first 6 months:
After second 6 months:
Total interest from second investment = $10,816 - $10,000 = $816
Step 3: Sum the Interest Amounts
Total interest earned = $480 + $816 = $1,296
Answer: E
The key insight: Notice how compound interest means the principal grows after each compounding period. In the second 6-month period, you're earning interest on $10,400, not the original $10,000. That's the power of compounding - your interest earns interest!
You can explore the complete solution with the systematic framework for tackling all interest calculation problems here on Neuron by e-GMAT. You can also access detailed solutions for other official questions on Neuron to build consistent accuracy across all quant topics.
Here's how to approach this:
Understanding the Setup
Kevin made two separate investments:
- $8,000 at 6% simple interest for 1 year
- $10,000 at 8% compounded semiannually for 1 year
The key thing you need to recognize is that these require different calculation approaches - one is simple interest, the other is compound interest.
Step 1: Calculate Simple Interest (First Investment)
For simple interest, you just calculate a percentage of the original amount. Nothing more, nothing less.
Kevin invested $8,000 at 6% for 1 year.
Interest = \(0.06 \times 8,000 = 480\)
So Kevin earned $480 from his first investment.
Step 2: Calculate Compound Interest (Second Investment)
Now here's where it gets interesting. "Compounded semiannually" means the interest is calculated and added to the account twice per year - every 6 months.
Since the annual rate is 8%, each 6-month period earns 4% interest (because 8% ÷ 2 = 4%).
Let me show you what happens step by step:
After first 6 months:
- Starting amount: $10,000
- Interest earned: \(0.04 \times 10,000 = 400\)
- New balance: $10,000 + $400 = $10,400
After second 6 months:
- Starting amount: $10,400 (notice we're now using the updated amount!)
- Interest earned: \(0.04 \times 10,400 = 416\)
- Final balance: $10,400 + $416 = $10,816
Total interest from second investment = $10,816 - $10,000 = $816
Step 3: Sum the Interest Amounts
Total interest earned = $480 + $816 = $1,296
Answer: E
The key insight: Notice how compound interest means the principal grows after each compounding period. In the second 6-month period, you're earning interest on $10,400, not the original $10,000. That's the power of compounding - your interest earns interest!
You can explore the complete solution with the systematic framework for tackling all interest calculation problems here on Neuron by e-GMAT. You can also access detailed solutions for other official questions on Neuron to build consistent accuracy across all quant topics.
