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Mr. Kheung had 2,000 dollars to invest. He invested part of it at 5% per year and the remainder at 4% per year. After one year, his investment grew to 2,095 dollars. How much of the original investment was at the 5% rate?

 Jan 31, 2021
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Mr. Kheung had 2,000 dollars to invest. He invested part of it at 5% per year and the remainder at 4% per year. After one year, his investment grew to 2,095 dollars. How much of the original investment was at the 5% rate?     

 

Assuming simple interest

 

Let the amount invested at 5% per year be represented by X 

Let the amount invested at 4% per year be represented by 2,000 – X  

The total interest is the final value less the principal which is 2,095 – 2,000 = 95

 

The total interest is the sum of the two investments  

 

(0.05)(X) + (0.04)(2,000 – X)  =  95  

 

Can you take it from there?  Solve for X.  Go ahead and try. and use the following to check your answer.  

 

 

                                           (0.05)(X) + (0.04)(2,000 – X)  =  95  

 

                                                              .05X + 80 – .04X  =  95     

 

Combine the X's to get .01X  

and subtract 80 from each side                                 .01X  =  15  

 

Divide both sides by .01                                                  X  =  1500  invested at 5%   

.

 Jan 31, 2021

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