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Susie Q has 1000 dollars to invest. She invests some of the money at the Pretty Penny Bank, which compounds annually at 3 percent. She invests the rest of the money at the Five and Dime Bank, which compounds annually at 5 percent. After two years, Susie has a total of $1090.02. How much did Susie Q originally invest at the Pretty Penny Bank, in dollars?

 
Guest Aug 12, 2017
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Let the amount she invested at Pretty Penny  = x

So...we can call the amount invested at Five and dime  = 1000 - x

 

So....amt  invested at each bank * compounding for 2 years  = final amount     ....and we have that...

 

x(1.03)^2 + (1000 - x) (1.05)^2  = 1090.02      simplify

 

1.0609x   + (100 - x) (1.1025 )  = 1090.02

 

1.0609x  +  1102.5  -  1.1025x  =  1090.02      combine like terms on the left

 

- .0416x  + 1102.5  =  1090.02           subtract   1102.5 from each side

 

- .0416x    =  -12.48              divide both sides by -.0416

 

x  = $300  invested at Pretty Penny

 

and

 

(1000 - x )  = (1000 - 300)  = $700  invested at Five and Dime 

 

 

 

cool cool cool

 
CPhill  Aug 12, 2017

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