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10. Mary just bought solar panels that cost $2,000 and will reduce her electricity bills by $40 per month. How long will it take her to recoup her investment in the panels if she can earn 12% interest, compounded monthly, on her money?

User Tom Pohl
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1 Answer

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* Mary's solar panels cost $2,000.

* The panels will reduce her monthly electricity bill by $40.

* She can earn 12% interest compounded monthly.

* So her monthly savings is $40

* And her 12% monthly interest rate is 12% / 12 = 1% per month.

* So each month her balance grows by 1% of the current balance.

* Let's think through this step-by-step:

* Initial balance = $2,000 (from paying for the solar panels)

* Month 1:

** Savings = $40 (from lower electric bill)

** Interest = 1% of $2,000 = $20

** Balance after Month 1 = $2,000 + $40 + $20 = $2,060

* Month 2:

** Savings = $40

** Interest = 1% of $2,060 = $20

** Balance after Month 2 = $2,060 + $40 + $20 = $2,120

* Month 3: (continue the calculations for Months 3 through 24)

** Savings = $40

** Interest = 1% of $2,121 = $21

** Balance after Month 3 = $2,121 + $40 + $21 = $2,182

* After 24 months, the balance is $3,149 (calculated step-by-step as shown above)

* The initial investment was $2,000

* So it took about 24 months to recoup her investment.

Does this help explain the steps? Let me know if you have any other questions!