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Question 1170948: A man would like to invest P 50,000 in government bonds and stocks that will give an
overall annual return of about 5%. The money to be invested in government bonds will
give an annual return of 4.5% and the stocks of about 6%. The investments are in units
of P 100.00 each. If he desires to keep his stock investment to minimum in order to
reduce his risk, determine how many government bonds and how many stocks should he
purchase.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's solve this problem step-by-step.
**1. Define Variables:**
* Let 'x' be the number of units of government bonds.
* Let 'y' be the number of units of stocks.
**2. Set Up Equations:**
* **Total Investment:** The total investment is P 50,000, and each unit is P 100.00.
* 100x + 100y = 50,000
* Divide by 100: x + y = 500 (Equation 1)
* **Annual Return:** The desired overall return is 5% of P 50,000, which is P 2,500.
* 4.5% of (100x) + 6% of (100y) = 2,500
* 4.5x + 6y = 2,500 (Equation 2)
**3. Solve the System of Equations:**
We can solve this system using substitution or elimination. Let's use substitution:
* From Equation 1: y = 500 - x
* Substitute this into Equation 2:
* 4.5x + 6(500 - x) = 2,500
* 4.5x + 3,000 - 6x = 2,500
* -1.5x = -500
* x = 500 / 1.5 = 1000 / 3 ≈ 333.33
Since the investments are in whole units, we need to round to the nearest whole number. We'll round down to minimize stock investment, so x = 333.
* Substitute x = 333 back into Equation 1:
* 333 + y = 500
* y = 500 - 333 = 167
**4. Check the Solution:**
* Total Investment: 333(100) + 167(100) = 33,300 + 16,700 = 50,000 (Correct)
* Annual Return:
* (0.045 * 33,300) + (0.06 * 16,700) = 1,498.50 + 1,002 = 2,500.50
The return is slightly over P 2,500, which is acceptable.
**5. Conclusion:**
The man should purchase:
* **333 units of government bonds (P 33,300)**
* **167 units of stocks (P 16,700)**
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