The monthly membership fee of the gymnasium was $95 three years ago. The fee has since had annual increases of 2.8%, 5.5% and 3.3% respectively. Total percentage increase in fees over the three years is closest to:

Question

BlackTom AI · Accepted Answer

The problem asks for the total percentage increase in the gym membership fee after three consecutive annual increases of 2.8%, 5.5%, and 3.3%. Rather than simply adding the percentages, the increases compound year to year, so we multiply the factors for each year.

First, convert each percentage increase to a growth factor:
- Year 1: 2.8% increase corresponds to a factor of 1 + 0.028 = 1.028
- Year 2: 5.5% increase corresponds to a factor of 1 + 0.055 = 1.055
- Year 3: 3.3% increase corresponds to a factor of 1 + 0.033 = 1.033

Next, multiply the factors to get the overall growth factor over the three years:
Overall factor = 1.028 × 1.055 × 1.033
Compute step by step: 1.028 × 1.055 ≈ 1.08454
Then 1.08454 × 1.033 ≈ 1.12033

The total percentage increase is (Overall factor − 1) × 100% ≈ (1.12033 − 1) × 100% ≈ 0.12033 × 100% ≈ 12.033%

Thus, the total percentage increase in fees over the three years is approximately 12.03%.

If you were comparing to a multiple-choice set, you would look for the option closest to 12.03%. Since the options are not provided here, this calculation shows the exact cumulative effect of the three successive increases rather than a simple sum of percentages.

MCD1550 / MCD2140 - T1 - 2025 TEST 3 (Week 8)

The monthly membership fee of the gymnasium was $95 three years ago. The fee has since had annual increases of 2.8%, 5.5% and 3.3% respectively. Total percentage increase in fees over the three years is closest to:

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