Paying back a roof
Carrying one annual figure through four questions, where using the wrong base at step two spoils steps three and four.
Scenario
A household installs solar panels for £6,400. Before installation the household paid £1,150 a year for electricity. Afterwards it pays £340 a year, and it receives £180 a year for electricity it exports back to the grid.
The panels are guaranteed for 25 years. Assume prices and usage stay the same.
Answers in order, explanations withheld, and a report on where the chain broke.
- 6.1RatesFoundation
By how much does the household's electricity bill fall each year?
- A£810
- B£990
- C£340
- D£1,150
Show the answer and reasoningHide the reasoning
£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.
- 6.2RatesStandard
Builds on: 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?
- A£990
- B£810
- C£1,330
- D£520
Show the answer and reasoningHide the reasoning
£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.
- 6.3RatesChallenge
Builds on: 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?
- AAbout 6.5 years
- BAbout 7.9 years
- CAbout 5.6 years
- DAbout 12.3 years
Show the answer and reasoningHide the reasoning
About 6.5 years
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.
- 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.
Over the full 25-year guarantee, what is the household's net position?
- AAbout £18,350 ahead
- BAbout £24,750 ahead
- CAbout £6,400 ahead
- DAbout £20,250 ahead
Show the answer and reasoningHide the reasoning
About £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.