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Company expenses were 2,000, 2,200, 2,420, and 2,662 for four years. What is the estimated project expense of the sixth year?
3200
3221
3500
3250
3221
Observe the growth: 2000 to 2200 is a 10 percent increase (multiply by 1.1). Apply the same 1.1 multiplier repeatedly to find subsequent terms.
Observe the growth: 2000 to 2200 is a 10 percent increase (multiply by 1.1). Apply the same 1.1 multiplier repeatedly to find subsequent terms.
Analyze the common ratio
Calculate the multiplier for consecutive terms: 2200 / 2000 = 1.1, 2420 / 2200 = 1.1, and 2662 / 2420 = 1.1. The series follows a geometric progression with a common ratio of 1.1.
Calculate fifth and sixth year expenses
Fifth year = 2662 multiplied by 1.1 = 2928.2. Sixth year = 2928.2 multiplied by 1.1 = 3221.02, which rounds to 3221.
A: 3200 is too low based on the 1.1 compounding logic; C: 3500 is mathematically inconsistent with the established 10 percent growth; D: 3250 exceeds the accurate calculation result of 3221.
B is correct because the series increases by exactly 10 percent each year (multiplied by 1.1), leading to 2928.2 for year five and 3221.02 (rounded to 3221) for year six.
When terms in a series increase by small, varying amounts, check for percentage growth ratios (1.05, 1.1, 1.2) before looking for additive differences.
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