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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

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

Full solution

Q. The cumulative costs of a tankless water heater and tank water heater are $4,090 \$ 4,090 each at the end of the 7th  7^{\text {th }} year of use. The cumulative costs of the tankless heater increase $180 \$ 180 per year, but for the tank heater, they increase by 11% 11 \% per year. By the end of the 10th  10^{\text {th }} year, about how much more will the cumulative costs of the tank heater be than those of the tankless heater?\newlineChoose 11 answer:\newline(A) $964 \$ 964 \newline(B) $1,504 \$ 1,504 \newline(C) $4,625 \$ 4,625 \newline(D) $5,723 \$ 5,723
  1. Calculate Cumulative Cost: Determine the cumulative cost of the tankless water heater after 1010 years.\newlineWe know that the cumulative cost of the tankless water heater is $4,090\$4,090 at the end of the 77th year and it increases by $180\$180 per year. Therefore, we need to calculate the cost for 33 more years (88th, 99th, and 1010th year).\newlineCumulative cost after 1010 years = $4,090+3×$180\$4,090 + 3 \times \$180
  2. Perform Calculation: Perform the calculation for the tankless water heater.\newlineCumulative cost after 1010 years = $4,090\$4,090 + 33 * $180\$180 = $4,090\$4,090 + $540\$540 = $4,630\$4,630
  3. Determine Tank Water Heater Cost: Determine the cumulative cost of the tank water heater after 1010 years.\newlineThe cumulative cost of the tank water heater is also $4,090\$4,090 at the end of the 77th year and it increases by 1111\% per year. We need to calculate the increased cost for the 88th, 99th, and 1010th years.\newlineFor the 88th year: $4,090×1.11\$4,090 \times 1.11\newlineFor the 99th year: ($4,090×1.11)×1.11(\$4,090 \times 1.11) \times 1.11\newlineFor the 1010th year: (($4,090×1.11)×1.11)×1.11((\$4,090 \times 1.11) \times 1.11) \times 1.11
  4. Perform Tank Water Heater Calculation: Perform the calculation for the tank water heater.\newlineFor the 88th year: $4,090×1.11=$4,539.90\$4,090 \times 1.11 = \$4,539.90\newlineFor the 99th year: $4,539.90×1.11=$5,039.299\$4,539.90 \times 1.11 = \$5,039.299\newlineFor the 1010th year: $5,039.299×1.11$5,593.62\$5,039.299 \times 1.11 \approx \$5,593.62
  5. Calculate Cost Difference: Calculate the difference in cumulative costs after 1010 years.\newlineDifference = Cumulative cost of tank heater after 1010 years - Cumulative cost of tankless heater after 1010 years\newlineDifference $5,593.62$4,630\approx \$5,593.62 - \$4,630
  6. Final Calculation: Perform the final calculation to find the difference.\newlineDifference \approx $5,593.62\$5,593.62 - $4,630\$4,630 \approx $963.62\$963.62

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