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You pay $21,600 to the Laramie Fund, which has a NAV of $18 per share at the beginning of the year. The fund deducted a front-end load of 4%. The securities in the fund increased in value by 10% during the year. The fund's expense ratio is 1.3% and is deducted from year-end asset values. What is your rate of return on the fund if you sell your shares at the end of the year?

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MrRoyal

Answer:

4.23%

Explanation:

Given

Investment = $21,600

Front-end load = 4%

Rate of return is calculated by:

End investment - Beginning investment/ Beginning investment

First we calculate the available fund.

This is calculated as:

Available fund= Investment x (1- Front-end load %)

Available Fund = $21,600 x (1 - 4%)

Available Fund = $21,600 * (1 - 0.04)

Available Fund = $20,736

Then we Calculate the number of shares.

This is given by;

Shares= Available Fund/NAV

Where NAV = $18 Per share

Shares =$20,736/$18 per share

Shares = 1,152 shares

The NAV end is then calculated.

This is calculated by;

NAV End =NAV Begining * (1+ Growth rate)

NAV End =$18 *(1+.10)

NAV End = $18 * 1.10

NAV End =$19.80

The Year end asset value is then calculated by

Assets Value = NAV end * number of shares

Assets Value =$19.80 x 1,152

Assets Value = $22,809.60

The end investment is also calculated by;.

End investment=year end asset value x (1- expense ratio)

End Investment =$22,809.60 x (1-.013)

End Investment =$22,513.08

Lastly, End investment - Beginning investment/ Beginning investment

=(22,513.08-21,600)/21,600

=0.0423

= 4.23%

The rate of return is the percentage that is charged over the invested amount by the investor. It is the interest rate at which the investor will gain returns over the funds invested at the end of each period or as per the return payment period decided.

The rate of return on the fund when the shares are sold at the end of the year is 4.23%.

Computation:

Given:

Fund invested or principle amount =$21,600

NAV at beginning =$18 per share

Front-end load =4%

Fund expense ratio =1.3%

% increase in the value of fund =10%

1. Computation of available funds:

[tex]\text{Available Fund}=\text{Investment}\times(1-\text{Front end load})\\=\$21,600\times(1-0.04)\\=\$21,600\times0.06\\=\$20,736[/tex]

2. Computation of number of shares:

[tex]\text{Number of Shares}=\dfrac{\text{Available fund}}{\text{NAV}}\\=\dfrac{\$20,736}{\$18}\\=1,152\;\text{shares}[/tex]

3. Computation of NAV at the year-end:

[tex]\text{NAV at end}=\text{NAV at beginning}\times(1+\text{growth rate})\\=\$18\times(1+0.10)\\=\$18\times1.10\\=\$19.80[/tex]

4. Computation of ending asset value:

[tex]\text{Year-end asset value}=\text{NAV at end}\times\text{Number of shares}\\=\$19.80\times1,152\\=\$22,809.60[/tex]

5. Computation of ending investment:

[tex]\text{Ending Investment}=\text{Year-end asset value}\times(1-\text{fund expense ratio})\\=\$22,809.60\times(1-0.013)\\=\$22,513.08[/tex]

6. Computation of interest rate of return:

[tex]\text{Rate of return}=\dfrac{\text{Ending investment-Beginning Investment}}{\text{Beginning Investment}}\\=\dfrac{\$22,513.08-\$21,600}{\$21,600}\\=0.0423\;\text{or}\;4.23\%[/tex]

To know more about the rate of return, refer to the link:

https://brainly.com/question/13821923

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