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