Question

a married couple buys 280 shares of stock for a total investment of $8,722. they decide to sell all of their shares in the fund at the listing value shown below.

name of fund	nav	offer price

determine if the couple makes a profit or loss, and how much per share.
a. loss of $0.05 per share
b. loss of $0.10 per share
c. profit of $0.05 per share
d. profit of $0.10 per share

Explanation:

Step1: Calculate cost per share

The total investment is $8,722 for 280 shares. So cost per share is $\frac{8722}{280} = 31.15$.

Step2: Compare with NAV (selling price per share)

NAV is $31.05. Cost per share is $31.15, selling price is $31.05. So loss per share is $31.15 - 31.05 = 0.10? Wait, no, wait. Wait, when selling, do they sell at NAV or Offer Price? Wait, the problem says "sell all of their shares in the fund at the listing value shown below". Wait, the table has NAV and Offer Price. Wait, maybe I misread. Wait, the couple bought the shares, so their cost per share is total investment divided by number of shares. Then, when selling, they sell at NAV? Or Offer Price? Wait, the problem says "sell all of their shares in the fund at the listing value shown below". Wait, maybe the NAV is the selling price? Wait, let's re-express.

Wait, the couple buys 280 shares for $8,722. So cost per share: $8722 / 280. Let's calculate that: 8722 ÷ 280. 280 × 31 = 8680. 8722 - 8680 = 42. 42 / 280 = 0.15. So cost per share is $31.15. Now, when they sell, what's the price? The table has NAV $31.05 and Offer Price $31.20. Wait, maybe when selling mutual funds, you sell at NAV. So selling price per share is $31.05. Then, cost per share is $31.15. So loss per share is 31.15 - 31.05 = $0.10? Wait, no, wait, maybe I messed up the buying price. Wait, maybe the offer price is the buying price? Wait, the couple bought the shares, so maybe they bought at offer price? Wait, no, the total investment is $8,722 for 280 shares. Let's check: 280 × 31.20 = 8736, which is more than 8722. 280 × 31.15 = 8722. So their cost per share is $31.15. Now, when selling, they sell at NAV, which is $31.05. So the loss per share is 31.15 - 31.05 = $0.10? Wait, but let's check again. Wait, maybe the selling price is NAV, buying price is their cost per share. So cost per share: 8722 / 280 = 31.15. Selling price per share: 31.05. So loss of 31.15 - 31.05 = 0.10 per share. Wait, but the options have loss of $0.10 per share (option b) or loss of $0.05 (a), profit 0.05 (c) or 0.10 (d). Wait, maybe I made a mistake. Wait, let's recalculate cost per share: 8722 divided by 280. Let's do 8722 ÷ 280. 280 × 31 = 8680. 8722 - 8680 = 42. 42 ÷ 280 = 0.15. So 31 + 0.15 = 31.15. So cost per share is $31.15. Now, the NAV is $31.05. So when they sell, they get $31.05 per share. So the difference is 31.15 - 31.05 = $0.10 loss per share. So option b.

Answer:

b. loss of $0.10 per share