Quarterly growth rates are 2%, -1%, 3%, and 4%. What is the approximate cumulative annual growth?

Quarterly growth rates are 2%, -1%, 3%, and 4%. What is the approximate cumulative annual growth?

• A. About 6.5%
• B. About 8.2%
• C. About 10%
• D. About 2%

Answer: (B)

Growth compounds over time, so you combine quarterly changes by multiplying their growth factors. Turn each rate into a factor: 1.02, 0.99, 1.03, 1.04. Multiply in order: 1.02 × 0.99 = 1.0098; 1.0098 × 1.03 = 1.040094; 1.040094 × 1.04 = 1.08169776. Subtract 1 to get the annual growth: 0.08169776, about 8.17%, which rounds to roughly 8.2%. The slight edge over 8% comes from compounding across quarters. Relying on simple addition would miss this small compounding effect.

Growth compounds over time, so you combine quarterly changes by multiplying their growth factors. Turn each rate into a factor: 1.02, 0.99, 1.03, 1.04. Multiply in order: 1.02 × 0.99 = 1.0098; 1.0098 × 1.03 = 1.040094; 1.040094 × 1.04 = 1.08169776. Subtract 1 to get the annual growth: 0.08169776, about 8.17%, which rounds to roughly 8.2%. The slight edge over 8% comes from compounding across quarters. Relying on simple addition would miss this small compounding effect.