The cumulative costs of a tankless water heater and tank water heater are $4,090 each at the end of the 7^("th ") year of use. The cumulative costs of the tankless heater increase $180 per year, but for the tank heater, they increase by 11% per year. By the end of the 10^("th ") year, about how much more will the cumulative costs of the tank heater be than those of the tankless heater? Choose 1 answer: (A) $964 (B) $1,504 (C) $4,625 (D) $5,723

Question

The cumulative costs of a tankless water heater and tank water heater are  $4,090 each at the end of the  7^("th ") year of use. The cumulative costs of the tankless heater increase  $180 per year, but for the tank heater, they increase by  11% per year. By the end of the  10^("th ") year, about how much more will the cumulative costs of the tank heater be than those of the tankless heater? Choose 1 answer: (A)  $964 (B)  $1,504 (C)  $4,625 (D)  $5,723

Bytelearn · Accepted Answer

Calculate Tankless Water Heater Cost: Determine the cumulative cost of the tankless water heater after 10 years. We know that the cumulative cost of the tankless water heater is $4,090 at the end of the 7th year. It increases by $180 per year. Therefore, for the next 3 years (8th, 9th, and 10th year), we need to add this annual increase to the initial cost. Cumulative cost after 10 years = Initial cost + (Annual increase × Number of years) = $4,090 + ($180 × 3) = $4,090 + $540 = $4,630Calculate Tank Water Heater Cost: Determine the cumulative cost of the tank water heater after 10 years. The cumulative cost of the tank water heater is also $4,090 at the end of the 7th year. It increases by 11% per year. We need to calculate the compound increase for the next 3 years. For the 8th year: $4,090 × (1 + 11/100) = $4,090 × 1.11 For the 9th year: ($4,090 × 1.11) × 1.11 For the 10th year: (($4,090 × 1.11) × 1.11) × 1.11 Cumulative cost after 10 years = $4,090 × (1.11)^3Calculate Tank Water Heater Compound Increase: Calculate the cumulative cost of the tank water heater after 10 years. Cumulative cost after 10 years = $4,090 × (1.11)^3 = $4,090 × 1.11 × 1.11 × 1.11 = $4,090 × 1.367631 ≈ $5,594.77Calculate Difference in Cumulative Costs: Calculate the difference in cumulative costs between the tank water heater and the tankless water heater after 10 years. Difference = Cumulative cost of tank heater - Cumulative cost of tankless heater = $5,594.77 - $4,630 ≈ $964.77

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