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%