Which option does not provide a benefit to investors purchasing a mutual fund?

The correct response accurately identifies "churning" as the option that does not provide a benefit to investors purchasing a mutual fund. Churning refers to the excessive buying and selling of securities in a client's account, primarily executed by a broker to generate commissions. This practice is detrimental to investors as it increases transaction costs and may lead to poor investment returns due to frequent trading, undermining the long-term growth potential of the investment.

In contrast, the other options—rights of accumulation, letter of intent, and breakpoint—offer significant benefits to investors. The rights of accumulation allow investors to combine their purchases across different funds to qualify for reduced sales charges. A letter of intent enables investors to commit to invest a specified amount over a period, allowing them to take advantage of breakpoints and reduce the cost of their investment. Breakpoints are thresholds at which the sales charges on mutual fund purchases decrease, encouraging larger investments and making them more cost-effective. Each of these options supports the investor's overall financial goals, further highlighting why churning is not beneficial in the context of mutual fund investments.