An apartment association lets its members pay 11 months of their monthly maintenance fee in lumpsum, while the usual option of monthly payments also exists. The treasurer claims that placing the 11-month lumpsum in a bank fixed deposit yields the same sum as 12 months of regular payment, as assessed at the year-end (assuming the monthly payments are not reinvested by the treasurer). What's the fixed deposit's rate of interest?

Let the monthly maintenance fee be $1$ unit.

With monthly payments, the treasurer collects $12 \times 1 = 12$ units over the year (not reinvested, so no interest earned).

With the lumpsum option, residents pay $11 \times 1 = 11$ units upfront, which is placed in an FD for 1 year.

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The treasurer claims both options yield the same amount at year-end:

$11(1 + r) = 12$

$1 + r = \dfrac{12}{11}$

$r = \dfrac{12}{11} - 1$

$r = \dfrac{1}{11}$

$r = 9.09\%$

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The fixed deposit's rate of interest is $9.09\%$.