# Solving Investment Problems

Updated on August 6, 2018

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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## Comments

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• abiola

16 months ago

a clark at the far east garments is paid 70 centavos for every piece he assembles. he is fined 80 centavos for every piece quality control rejects. in addition, he gets a daily allowance of php 12.50. at the end of a certain day,this worker finished 81 pcs.2 of which were rejected. how much was the gross pay for the day

• AUTHOR

Maria Cristina Aquino Santander

4 years ago from Manila

Great to hear that.

• thanks

4 years ago

:) this helped me a lot! :)

• denden mangubat

5 years ago from liloan, cebu, philippines

sorry i will read this next timebut i will bookmark this

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