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?

Rationale

36

To find the least number of months before the CDs from both banks mature at the same time, we need to calculate the least common multiple (LCM) of their maturity periods: 9 months and 12 months. The LCM of 9 and 12 is 36, meaning that both CDs will next mature together after 36 months.

A (72) YOUR ANSWER

This choice represents a possible maturity time that could occur, as both CDs would mature again after 72 months. However, it is not the least time; 36 months is the smallest interval during which both CDs will simultaneously mature.

B (36) CORRECT

This is the correct answer, as it is the least common multiple of 9 and 12. After 36 months, both CDs will have matured 4 times (for the 9-month CDs) and 3 times (for the 12-month CDs), aligning their maturity dates perfectly.

C (108) YOUR ANSWER

Although 108 months is a multiple of both 9 and 12, it is not the least common multiple. Thus, while it is a valid time frame for maturity alignment, it exceeds the required minimum of 36 months.

D (3) YOUR ANSWER

This option is incorrect because neither bank's CDs can mature at 3 months; the shortest maturity period is 9 months. Therefore, 3 months cannot represent a time when both CDs are mature.

Conclusion

The least number of months that will pass before the CDs from both banks mature at the same time is 36. This is derived from calculating the least common multiple of the two maturity periods, confirming that both CDs will align in their maturity schedules after this time.

36

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