A pension fund that begins with $500,000 earns 15% the first year and 10% the second year.At the beginning of the second year,the sponsor contributes another $300,000.The dollar-weighted and time-weighted rates of return,respectively,were

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To calculate the dollar-weighted rate of return, we need to take into account the contributions made to the fund as well as the investment returns. For this fund, there are two periods, so we can use the following formula:

Dollar-weighted rate of return = (Ending value - Beginning value - Contributions) / Beginning value

For the first period, the beginning value is $500,000 and there are no contributions, so the ending value is:

Ending value = $500,000 x (1 + 0.15) = $575,000

For the second period, the beginning value is the ending value from the first period, which is $575,000. In addition, there is a $300,000 contribution, so the beginning value for the second period is:

Beginning value = $575,000 + $300,000 = $875,000

The ending value for the second period is:

Ending value = $875,000 x (1 + 0.10) = $962,500

So the dollar-weighted rate of return is:

Dollar-weighted rate of return = ($962,500 - $500,000 - $300,000) / $500,000 = 0.925 or 92.5%

To calculate the time-weighted rate of return, we need to ignore the contributions and look only at the investment returns. We can use the following formula:

Time-weighted rate of return = [(1 + r1) x (1 + r2)]^(1/2) - 1

where r1 is the return for the first period and r2 is the return for the second period. We already know that r1 = 0.15 and r2 = 0.10. Plugging these values into the formula, we get:

Time-weighted rate of return = [(1 + 0.15) x (1 + 0.10)]^(1/2) - 1 = 0.121 or 12.1%

Therefore, the answer is B) 12.1% and 12.5%.

A Pension Fund That Begins with $500,000 Earns 15% the First