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Algebra/weighted averages


I have three types of investments.  50% of my portfolio is in a US bond fund.  40% is in a US stock fund.  10% is in an international stock fund. I have not bought or sold anything in 2013.

My bond fund (50%) has lost 2% this year.
My US stock fund(40%) has gained 38% this year.
My international stock fund (10%)has gained 34% this year.

If my total investments were worth $100 on January 1, 2013, what are they worth now.

If I had $100,000 on January 1, 2013, what is value be now?

If I had one million dollars on Jan 1, 2013, what is the value now?

Thank you.

Since the 2% was on 50% of the cash, the total is 50% of -2%, and that is -1%.
Since the 38% was on 40%, 40% of 38% is 15.2%.
Since 34% is on 10%, the total gain 10% of 34%, and that is 3.4%.
Thus, the total gain is the sum of -1% + 15.2% + 3.4% = 17.6%.

Since the investment was on Jan 1, 2013, I will assume one year has passed
(in just a few more months it will be a year).

For $100, the return would be $17.6.
For $100,000, the return would be $17,600.
For $1,000,000, the return would be $176,000.

As can be seen, they all of answers start with 176.
The digits to the left of the decimal are always one less than what the question puts in.

Technically, it is roughly 322/360 of one year.
that would make it be 294/365, which is roughly 80% of the year.
The interest would then be $14.17 per $100.


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Scott A Wilson


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