Exponential Growth and Decay • Topic 4 of 4

Financial Applications

Money invested at compound interest grows exponentially: A = P(1 + r)^t, with P the principal, r the annual rate as a decimal, and t the number of years. This is the same formula as population growth applied to dollars. For $1,000 at 20% compounded annually for 2 years, A = 1000(1.2)² = $1,440. The interest earned is the final amount minus the principal. Compounding means interest earns interest, so the total exceeds simple interest over the same period. Set up (1 + r)^t carefully and decide whether the question wants the total amount or just the interest. The SAT keeps the rates and years clean.

Compound interest growth curve rising above a straight dashed simple-interest lineCompound growthyearsamount ($)Compound interest grows faster than simple

✅ Solved examples

1. $1,000 at 20% compounded annually for 2 years. Amount?
1000(1.2)² = $1,440.
2. $2,000 at 10% for 2 years. Amount?
2000(1.1)² = $2,420.
3. $500 at 20% for 2 years. Amount?
500(1.2)² = $720.
4. $1,000 at 20% for 2 years. Interest earned?
Amount 1,440; interest 1440 − 1000 = $440.

✏️ Practice — try these, take hints as needed

1. $1,000 at 10% compounded annually for 2 years. Amount?
1000(1.1)².
1000 × 1.21.
—
$1,210.
2. $3,000 at 20% for 2 years. Amount?
3000 × 1.44.
—
—
$4,320.
3. $2,000 at 50% for 2 years. Amount?
2000 × 2.25.
—
—
$4,500.
4. $4,000 at 10% for 2 years. Amount?
4000 × 1.21.
—
—
$4,840.
5. $1,000 at 10% for 2 years. Interest earned?
Amount = 1,210.
1210 − 1000.
—
$210.

📝 Topic test — 8 questions

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