# Solving Investment Problems

**Solving Investment Problems**

**One of the most important applications of linear equations is found in solving investment problems. Investment problems use the Simple Interest formula I = Prt, where **

**P = Principal (Amount invested )**

**r = rate of simple interest**

**t = time in years**

**In this hub I present several problems with their solutions.**

**Problem Number One :**

**A man invested 35,000 pesos partly at 15% and the rest at 18%. The total income from these investments is 5,650 pesos. Find the sum invested at each rate.**

**Solution :**

**Let X = Amount invested at 15%**

**35,000 – X = Amount invested at 18%**

**Since Interest = Prt therefore**

**.15X = Interest earned at amount invested at 15%**

**.18(35,000 – X )= Interest earned at amount invested at 18%**

**Interest earned at 15% + Interest earned at 18% = 5,650**

**Working Equation :**

**.15X + .18(35,000 – X) = 5,650**

**Multiplying this equation by 100**

**15X + 18(35,000 – X ) = 565,000 **

**15X + 630,000 - 18X = 565,000**

**-3X = 565,000 – 630,000**

**(-3X = -65,000 ) -1/3**

**X = 21,667.67 ==****è Amount invested at 15%**

**35,000 – 21,666.67 = 13,3333.33 =****è Amount Invested at 18%**

**Problem Number Two :**

**A church congregation has 20,000 pesos to be invested in a fund , part at 3% and part at 7%. If the investment at 7% earns 500 pesos more per year than the other placement, how much is invested at each rate ?**

**Solution :**

**Let X = Amount invested at 3%**

**20,000 – X = Amount invested at 7%**

**Interest earned at 3% = .03X**

**Interest earned at 7% = .07( 20,000 – X )**

**Interest at 3% + 500 = Interest at 7%**

**Working equation :**

**.03X + 500 = .07(20,000 – X )**

**Multiplying this equation by 100**

**3X + 50,000 =7(20,000 –X )**

**3X + 50,000 = 140,000 – 7X**

**3X + 7X = 140,000 – 50,000**

**(10X = 90,000) 1/10**

**X = 9,000 =****è Amount invested at 3%**

**20,000 – 9,000 = 11,000 =****è Amount invested at 7%**

**Problem Number Three**

**Mr. Alfonso invested a sum of money at 4% simple interest and another sum which is 100,000 more than the first sum at 5%. The annual income from the two investments is 17,000 pesos. How much was Mr. Alfonso’s investment at each rate ?**

**Solution :**

**Let X = Amount invested at 4%**

**X + 100,000 = Amount invested at 5%**

**Interest at 4% = .04X**

**Interest at 5% = .05 (X + 100,000)**

**Interest at 4% + Interest at 5% = 17,000**

**Working equation :**

**.04X + .05(X + 100,000) = 17,000**

**Multiplying this equation by 100**

**4X + 5 ( X + 100,000) = 1,700,000**

**4X + 5X + 500,000 = 1,700,000**

**9X = 1,700,000 – 500,000**

**(9X = 1,200,000 ) 1/9**

**X = 133,333.33 =****è Amount invested at 4%**

**X + 100,000 = 133,333.33 + 100,000 = 233,333.33 ==****èAmount invested at 5%**

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