Question 91

Adrianne will take 8 months to repay the borrowed amount.

Adrianne's repayment strategy involves doubling the amount she pays back each month, starting from $1. By the 8th month, the cumulative total of her payments reaches $255, allowing her to fully repay the borrowed amount.

A) 8

This option is correct because, by the end of the 8th month, the payment sequence would be $1, $2, $4, $8, $16, $32, $64, and $128. Adding these amounts together results in a total of $255, which exactly matches the amount borrowed.

B) 10

This option is incorrect. If Adrianne took 10 months to repay, her total payments would exceed the borrowed amount significantly, as she would continue to double her payments beyond what is necessary to reach $255.

C) 16

This option is incorrect as well. By the 16th month, the cumulative payments would have greatly surpassed the borrowed amount due to the exponential growth in the payment amounts, making it unnecessary for her to take this long to repay.

D) 20

This option is also incorrect. Similar to option C, by the 20th month, the total amount paid would be excessively higher than the borrowed $255, indicating that this duration is not needed for repayment.

Conclusion

The analysis shows that 8 months is the precise duration required for Adrianne to repay her loan of $255 through her doubling payment method. All other options suggest durations that would lead to overpayment, failing to align with the repayment structure established by Adrianne.