The Smart-Thermostat Payback

The Smart-Thermostat Payback

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

The Smart-Thermostat Payback

The chapter’s human-centered example is a $250 smart thermostat in a home that spends $3,900 a year on heating and cooling and trims that bill by 30%. It argues the device sells itself because the payback lands in months, not years. This audit walks the payback line by line — annual saving, monthly saving, then months to break even — to ask exactly how fast a $250 device pays for itself.

Companion to the chapter What IoT Delivers — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is heating-cost saving. The middle card applies this page's rule. The green card is thermostat payback. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only heating-cost saving, so the numeric fixture does not switch without explanation.

Walk the arrows. A higher realised saving rate repays the same purchase price faster.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 30 %.

2. 2

   Name the relationship. payback = 250 x 12 / (3,900 x saving / 100)

3. 3

   Substitute with units. 250 x 12 / (3,900 x 30 / 100) = 2.56 months

4. 4

   Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change heating-cost saving

Try Predict the direction of payback = 250 x 12 / (3,900 x saving / 100). Test another heating-cost saving, then compare thermostat payback.

Heating-cost saving

30 %

Chapter baseline

Thermostat payback

Observe A higher realised saving rate repays the same purchase price faster. Reset heating-cost saving to 30 and compare thermostat payback.

Explain A higher realised saving rate repays the same purchase price faster.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only heating-cost saving moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only heating-cost saving. It is not a field prediction.

TryRecompute Annual savings: 3900 x 0.30 = 1170 dollars.

ObserveTrack Monthly savings: 1170 / 12 = 97.50 dollars.

ExplainExplain Payback period: 250 / 97.50 = 2.564 months, which rounds to 2.6 months.

Ready: use the stated baseline inputs, then compare each displayed result.

Ada: The chapter claims a $250 smart thermostat pays for itself in about 2.6 months for a home that spends $3,900 a year on heating and cooling and cuts that bill by 30%. Let me walk the payback all the way through.

• Annual savings: 3900 x 0.30 = 1170 dollars
• Monthly savings: 1170 / 12 = 97.50 dollars
• Payback period: 250 / 97.50 = 2.564 months, which rounds to 2.6 months.

A payback measured in weeks rather than years is exactly why this product sells itself — but the number is only as trustworthy as the 30% savings assumption underneath it, so the payback claim should always be quoted together with the efficiency figure it depends on.

Every number above is taken from the chapter’s own material and re-derived step by step.

Technical boundaries. This thermostat payback deliberately does not simulate weather, HVAC efficiency, tariff changes, or installation failures. It applies the fixed 30% saving to $3,900 annual heating cost and divides the $250 purchase by monthly savings.