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9 years ago Mary purchased shares in a certain mutual fund at Net Asset Value (NAV) of $60. She reinvested her dividends into the fund, and today she has 8.3% more shares than when she started. If the fund's NAV has increased by 41.3% since her purchase, compute the rate of return on her investment if she sells her shares today.Round your answer to the nearest tenth of a percent.

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Final answer:

Mary's rate of return on her investment, considering both the increased Net Asset Value and the reinvested dividends, is approximately 52.9%.

Step-by-step explanation:

First, we calculate the percentage increase in Mary's investment due to the increase in the Net Asset Value (NAV). If the NAV increased by 41.3% from $60, the new NAV is $60 + (41.3% of $60) = $60 + $24.78 = $84.78.

Now, we've also been told that Mary has 8.3% more shares than when she started, meaning the dividend reinvestment led to an increase in the number of shares without additional cost.

To determine the rate of return, we consider both the dividend reinvestments and the increase in NAV as part of the total return. The formula for the rate of return is:

Total Return = (Final Value of Investment - Initial Value of Investment) / Initial Value of Investment

Mary's initial investment value was simply the initial NAV times the original number of shares. Let's denote the original number of shares as 'S'. Hence her initial investment was $60 × S. Her final investment value is the new NAV multiplied by her increased number of shares, which is $84.78 × (S + 8.3% of S).

To find the rate of return, we'll calculate the percentage increase in the value of her total investment:

  1. Initial Investment = $60 × S
  2. Increased number of shares = S × (1 + 8.3/100) = 1.083S
  3. Final Investment = $84.78 × 1.083S
  4. Total Return = (Final Investment - Initial Investment) / Initial Investment
  5. Rate of Return = ((84.78 × 1.083S - 60S) / (60S)) × 100
  6. Rate of Return = ((91.75S - 60S) / 60S) × 100
  7. Rate of Return = (31.75 / 60) × 100
  8. Rate of Return = 52.92%

Therefore, the overall rate of return on Mary's investment, including both the increased NAV and Dividends, is approximately 52.9% (rounded to the nearest tenth of a percent).

User Douglas Tosi
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