With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

Question

BlackTom AI · Accepted Answer

When analyzing compounding frequencies, the key idea is that interest is added to the balance more often with higher-frequency compounding, which in turn earns interest in the next period. 
Option: daily. The reasoning here is that daily compounding updates the balance each day, so the interest from each day itself earns interest sooner, leading to the largest ending balance among the given options. 
Option: monthly. While monthly compounding does increase the balance more often than quarterly or annual compounding, it cannot surpass daily compounding because there are fewer compounding moments per year for interest to be added and earn future interest. 
Option: quarterly. Quarterly compounding occurs four times a year; this means even longer gaps between interest postings than monthly or daily, resulting in a smaller accumulated amount than higher-frequency options, assuming the rate and principal are the same. 
Option: annually. Annual compounding posts interest once per year, so none of the year’s interest is able to earn interest within the same year, producing the smallest ending balance among these choices when all other factors are equal. 
In summary, increasing the frequency of compounding generally increases the ending balance because interest is credited more often and has more opportunities to compound, making daily the option that yields the greatest ending balance in this set.

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?单项选择题

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