Question

XYZ Mutual Fund, an open-end investment company, has an NAV of $20 and a public offering price of $21.40. The prospectus states that the sales charge for purchases of fund shares of $25,000 through $49,999 is 4%. Approximately how many shares can the customer buy for $35,000?

A. 1,600 shares
B. 1,635 shares
C. 1,680 shares
D. 1,750 shares

Answer 1

To calculate the approximate number of shares a customer can buy with $35,000 in the XYZ Mutual Fund, we first find the actual cost per share including the sales charge. Afterward, we divide the total investment by this actual purchase price, which results in the purchase of approximately 1,682 shares.

Step-by-step explanation:

The XYZ Mutual Fund, an open-end investment company, has a net asset value (NAV) of $20 and a public offering price of $21.40 due to the sales charge. To calculate how many shares one can buy with $35,000 when the sales charge is 4%, we must first find out the actual cost per share that the investor pays, which is the public offering price. We use this formula:

Sales Charge = Public Offering Price - NAV

Then,

Actual Purchase Price including Sales Charge = NAV + (NAV * Sales Charge Percentage)

So, for this case:

Actual Purchase Price including Sales Charge = $20 + ($20 * 0.04) = $20.80

To determine the number of shares one can purchase, we divide the total investment by the actual purchase price:

Number of Shares = Total Investment / Actual Purchase Price

Number of Shares = $35,000 / $20.80 ≈ 1,682.69 shares

Since we cannot purchase a fraction of a share in an open-end fund, the customer can buy approximately 1,682 shares of the XYZ Mutual Fund with $35,000.