Adrianne borrowed $255, repaying $1, $2, $4, etc., doubling each month. How many months to repay?
Adrianne will take 8 months to fully repay the borrowed amount.
Adrianne's repayment schedule follows a geometric progression where each month she doubles the amount paid. Starting with $1 and doubling each month means the total repayment reaches $255 after 8 months.
In the first month, Adrianne pays $1, the second month $2, the third month $4, and so on. The amounts she pays each month form the series: $1, $2, $4, $8, $16, $32, $64, $128. By the end of the eighth month, she has repaid a total of $255, precisely covering the borrowed amount.
If Adrianne took 10 months, she would pay $1, $2, $4, $8, $16, $32, $64, $128, $256, and $512 in the ninth month. This total far exceeds the amount borrowed and does not reflect the correct timeline for repayment, as the debt is settled at the end of the eighth month.
A 16-month repayment period would imply she continues to double her payments beyond necessity. By this time, she would have paid a significantly larger sum, totaling in the thousands, far exceeding the $255 borrowed, making this option incorrect.
Choosing 20 months would similarly result in an overpayment, as the repayment would balloon to amounts that are impractical compared to the original loan. The doubling nature of the payments means that the debt is settled well before 20 months, rendering this option inaccurate.
Adrianne's repayment strategy results in a total of $255 being paid off in 8 months through exponential growth in her payments. Each month, doubling her previous payment leads to a swift repayment, illustrating how quickly debts can be settled with an increasing payment strategy. The other options misinterpret the repayment timeline, resulting in an overestimation of the months needed to clear the loan.
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