A private equity fund was reported to have an IRR of $15\%$ over its $8$ year life span. You know that they makde an acquisition when the fund started from which they received a dividend $6$ months later. In the IRR calculation, what annualized reinvestment return was assumed on that dividend until the end of the $8$ year period?

The average risk free rate for that time period of $5\%$

The internal rate of return of $15\%$

The weighted average cost of capital of the acquired company of $12\%$

The S&P $500\text{'}$s annualized return for that period of $7\%$