34. At a local bank, certificates of deposit (CDs) mature every 9 months. At another bank, CDs mature every 12 months. If CDs are purchased on the same day at each bank and are renewed when they mature, what is the least number of months that will pass before the two banks' CDs are mature at the same time?
Answer: B
The least number of months that will pass before the two banks' CDs are mature at the same time is 36.
The CDs from the local bank mature every 9 months, while the other bank's CDs mature every 12 months. To find the least common multiple of these two maturity periods, we determine that 36 months is the first point at which both CDs will mature together.
A) 72
While 72 months is a multiple of both 9 and 12, it is not the least number of months where both CDs will mature simultaneously. It represents a later point in time when the CDs would mature together again, rather than the earliest occurrence.
B) 36
This is the first instance where both CDs mature at the same time. The least common multiple of 9 and 12 is indeed 36, confirming that both banks' CDs will coincide in maturity after 36 months.
C) 108
Similar to option A, 108 months is a common multiple of both maturity periods but not the least. It represents a later point in time when both CDs would again be mature together, rather than the first occurrence.
D) 3
Three months does not align with the maturity schedules of either bank's CDs. Since the local bank's CDs mature every 9 months, they will not be mature at 3 months, making this option incorrect.
Conclusion
The correct answer is 36 months, as it is the least common multiple of the two maturity periods, ensuring that both banks' CDs will mature simultaneously for the first time. All other options either represent later occurrences or do not align with the specified maturity periods.