* 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!