A vocational course has seats that increase by 15% annually. If there were 800 seats in 1992, how many seats will there be in 1994 (after two annual increases)?

Introduction / Context:This compounding growth problem involves applying the same percentage increase year over year. It mirrors practical scenarios like enrollment growth, population increases, or asset appreciation over discrete periods.

Given Data / Assumptions:Initial seats (1992) = 800. Annual increase = 15% each year. We need the count in 1994, meaning two compounding steps (1992 → 1993 → 1994).

Concept / Approach:Use the compound factor (1 + r)^n where r = 0.15 and n = 2 years. The 1994 seats = 800 * 1.15 * 1.15. Compute sequentially to avoid rounding errors.

Step-by-Step Solution:

Verification / Alternative check:Direct compounding: 800 * (1.15)^2 = 800 * 1.3225 = 1058 (exact integer due to the given numbers).

Why Other Options Are Wrong:920 is after one year, not two. 1040 and 1060 are near misses from rough approximations. 1178 overshoots, reflecting a larger rate or extra year.

Common Pitfalls:Applying the increase only once, or adding 15% + 15% to get 30% and computing 800 * 1.30 = 1040 (approximate but not correct under compounding).

Final Answer:1058