Financial Mathematics • Topic 2 of 6

Compound Interest

Compound interest pays interest on both the principal and previously earned interest, so it grows faster than simple interest. Compounded annually, the amount after t years is A = P(1 + r)^t, with r the rate as a decimal. For $1,000 at 10% for 2 years, A = 1000(1.1)² = 1000 × 1.21 = $1,210 — that is $10 more than simple interest would give, because the second year earns interest on the first year’s interest. Square or raise (1 + r) to the correct power for the number of periods. The SAT favours small time spans so the arithmetic stays clean.

Amount versus years: a gray dashed straight line for simple interest and a blue curve for compound interest rising above itCompound interestYearsAmountSimpleCompoundCompound grows on interest already earned

✅ Solved examples

1. $1,000 at 10% compounded annually for 2 years. Amount?
1000(1.1)² = 1000 × 1.21 = $1,210.
2. $2,000 at 20% for 2 years. Amount?
2000(1.2)² = 2000 × 1.44 = $2,880.
3. $400 at 50% for 2 years. Amount?
400(1.5)² = 400 × 2.25 = $900.
4. How much interest does $1,000 at 10% earn over 2 years compounded?
Amount 1,210; interest 1210 − 1000 = $210.

✏️ Practice — try these, take hints as needed

1. $500 at 10% compounded annually for 2 years. Amount?
A = P(1 + r)².
500 × 1.21.
—
$605.
2. $1,000 at 20% for 2 years. Amount?
1000 × 1.44.
—
—
$1,440.
3. $800 at 50% for 2 years. Amount?
800 × 2.25.
—
—
$1,800.
4. $2,000 at 10% for 2 years. Amount?
2000 × 1.21.
—
—
$2,420.
5. $1,000 at 20% for 2 years. How much interest is earned?
Amount = 1,440.
1440 − 1000.
—
$440.

📝 Topic test — 8 questions

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