Paying back a roof

Paying back a roof

Carrying one annual figure through four questions, where using the wrong base at step two spoils steps three and four.

1. 6.1RatesFoundation

   By how much does the household's electricity bill fall each year?By how much does the household's electricity bill fall each year?

   • A$810$810
   • B$990$990
   • C$340$340
   • D$1,150$1,150
   Show the answer and reasoningHide the reasoning

   $810$810

   The bill falls from $1,150 to $340, a difference of $810. The export payment is not part of the bill and belongs in the next step, not this one.The bill falls from $1,150 to $340, a difference of $810. The export payment is not part of the bill and belongs in the next step, not this one.

2. 6.2RatesStandard

   Builds on: The $810 bill saving from question 1 — this step is that figure plus the export payment.The $810 bill saving from question 1 — this step is that figure plus the export payment.

   What is the household's total annual benefit from the panels?What is the household's total annual benefit from the panels?

   • A$990$990
   • B$810$810
   • C$1,330$1,330
   • D$520$520
   Show the answer and reasoningHide the reasoning

   $990$990

   The benefit is the bill saving plus the export payment: 810 + 180 = $990. Stopping at $810 leaves out money the household actually receives, and adding 180 to the full $1,150 double-counts the electricity still being paid for.The benefit is the bill saving plus the export payment: 810 + 180 = $990. Stopping at $810 leaves out money the household actually receives, and adding 180 to the full $1,150 double-counts the electricity still being paid for.

3. 6.3RatesChallenge

   Builds on: The $990 annual benefit from question 2. Using $810 instead produces one of the wrong choices here.The $990 annual benefit from question 2. Using $810 instead produces one of the wrong choices here.

   Roughly how many years does the installation take to pay for itself?Roughly how many years does the installation take to pay for itself?

   • AAbout 6.5 yearsAbout 6.5 years
   • BAbout 7.9 yearsAbout 7.9 years
   • CAbout 5.6 yearsAbout 5.6 years
   • DAbout 12.3 yearsAbout 12.3 years
   Show the answer and reasoningHide the reasoning

   About 6.5 yearsAbout 6.5 years

   6400990 is about 6.5 years. Using the $810 bill saving alone gives about 7.9 years, which is the answer available to anyone who stopped at question 1.6400/990 is about 6.5 years. Using the $810 bill saving alone gives about 7.9 years, which is the answer available to anyone who stopped at question 1.

4. 6.4Interpreting modelsChallenge

   Builds on: The $990 annual figure from question 2 again — and the reminder from question 3 that the $6,400 has to be paid back before anything is gain.The $990 annual figure from question 2 again — and the reminder from question 3 that the $6,400 has to be paid back before anything is gain.

   Over the full 25-year guarantee, what is the household's net position?Over the full 25-year guarantee, what is the household's net position?

   • AAbout $18,350 aheadAbout $18,350 ahead
   • BAbout $24,750 aheadAbout $24,750 ahead
   • CAbout $6,400 aheadAbout $6,400 ahead
   • DAbout $20,250 aheadAbout $20,250 ahead
   Show the answer and reasoningHide the reasoning

   About $18,350 aheadAbout $18,350 ahead

   Twenty-five years at $990 is $24,750, less the $6,400 cost, giving $18,350. Forgetting to subtract the installation gives $24,750, which is the total benefit rather than the net position.Twenty-five years at $990 is $24,750, less the $6,400 cost, giving $18,350. Forgetting to subtract the installation gives $24,750, which is the total benefit rather than the net position.