Answer:
time-weighted 12.5%
dollar-weighted 12%
Explanation:
time-weighted:
[tex]\sqrt{1.15 + 1.10} - 1 = 0.124722188 = 12.5[/tex]
Dollar-value
Return on dollars
[tex]500,000 \times 1.15 \times 1.10\\ = 632,500\\[/tex]
[tex]300,000 \times 1.1 = 330,000[/tex]
Present value of the return
[tex](632,500 + 330,000) \div (1+r)^2[/tex]
Present value of the investment:
[tex]500,000 + 300,000 \div (1+r)[/tex]
Both this concepts should match as they work with the same weighted rate
[tex]500,000 + 300,000 /(1+r) \times (1+r)^2 = 962,500\\500,000 (1+r)^2 + 300,000 (1+r) - 962,500 = 0[/tex]
We use cuadratic equation and solve getting a rate of 12%
