jmc

Question

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?

Accepted Answer

Let x be the number of dollars Susie Q invested at the Pretty Penny Bank. Then she invested 1000 - x at the Five and Dime Bank. After two years, her account at the Pretty Penny Bank has grown to x 1.03^2, and her account at the Five and Dime Bank has grown to (1000 - x) 1.05^2. Therefore, x 1.03^2 + (1000 - x) 1.05^2 = 1090.02.We see that x 1.03^2 + (1000 - x) 1.05^2 = 1.0609x + 1102.5 - 1.1025x = 1102.5 - 0.0416x, so 1102.5 - 0.0416x = 1090.02.Then x = 1102.5 - 1090.020.0416 = 300.