Word Problems & Translation • Topic 3 of 4

Interest & Growth

Interest and growth problems are translation applied to money and populations over time. Simple interest adds the same amount every period: I = P · r · t, where P is the principal, r the rate as a decimal, and t the time — so $2,000 at 5% for 3 years earns 2000 × 0.05 × 3 = $300. Compound interest instead multiplies each period: A = P(1 + r)ᵗ, so the same $2,000 at 5% compounded annually for 3 years grows to 2000 × 1.05³. Over the same terms, compound always yields more than simple, and the GRE loves a Quantitative Comparison contrasting the two. Population, depreciation, and "increases by x% each year" problems use the same compound multiplier — a decrease just makes the multiplier (1 − r). Keep the rate as a decimal and, since the basic on-screen calculator will not do exponents, expect small time periods (t = 2 or 3) so you can multiply the factor out by hand.

✅ Solved examples

1. Find the simple interest on $1,500 at 6% per year for 4 years.
I = P · r · t = 1500 × 0.06 × 4 = $360.
2. $1,000 is compounded annually at 10% for 2 years. Find the final amount.
A = 1000 × (1.10)² = 1000 × 1.21 = $1,210.
3. A town of 8,000 grows 5% per year. What is its population after 2 years?
8000 × (1.05)² = 8000 × 1.1025 = 8,820.
4. Quantitative Comparison. $1,000 for 2 years at 10% per year. Quantity A: total value under annual compounding. Quantity B: total value under simple interest. Which is greater?
Compound: 1000 × 1.21 = $1,210. Simple: 1000 + 1000 × 0.10 × 2 = $1,200. Quantity A is greater — compounding always beats simple over more than one period.

✏️ Practice — try these, take hints as needed

1. Simple interest on $2,500 at 4% for 3 years?
I = P · r · t.
2500 × 0.04 × 3.
Multiply.
$300
2. $5,000 compounded annually at 20% for 2 years — final amount?
A = P(1 + r)ᵗ.
5000 × 1.2².
5000 × 1.44.
$7,200
3. A $12,000 car depreciates 10% per year. Its value after 2 years?
Decrease means multiplier (1 − r) = 0.9.
12000 × 0.9².
12000 × 0.81.
$9,720
4. How much interest does $800 earn at 15% simple interest over 5 years?
P · r · t.
800 × 0.15 × 5.
Compute.
$600
5. A population of 2,000 grows 10% each year. Population after 3 years?
× 1.1 three times.
2000 × 1.331.
Multiply out.
2,662

📝 Topic test — 8 questions

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