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KiRa [710]
2 years ago
15

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
Business
1 answer:
Margaret [11]2 years ago
8 0

Answer:

time-weighted   12.5%

dollar-weighted 12%

Explanation:

<em><u>time-weighted:</u></em>

<em><u></u></em>\sqrt{1.15 + 1.10}  - 1 = 0.124722188 = 12.5<em><u></u></em>

<em>Dollar-value</em>

<em>Return on dollars </em>

<em></em>500,000 \times 1.15 \times 1.10\\ = 632,500\\<em></em>

<em></em>

<em></em>300,000 \times  1.1 = 330,000<em></em>

<u>Present value of the return</u>

(632,500 + 330,000) \div (1+r)^2

<u>Present value of the investment:</u>

<em></em>500,000  + 300,000 \div (1+r)<em></em>

<em></em>

<u>Both this concepts should match as they work with the same weighted rate</u>

<u />

<u />500,000 + 300,000 /(1+r)  \times (1+r)^2 = 962,500\\500,000 (1+r)^2 + 300,000 (1+r) - 962,500 = 0<u />

<u />

We use cuadratic equation and solve getting a rate of 12%

<u />

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