Question

Katie invested a total of $4000. Part at 4% simple interest and part at 5% simple interest. At the end of 1 year the investments had earned $175 interest. How much was invested at each rate?

Answer 1

Answer: $2500 at 4% and $1500 at 5%

Explanation:

`\begin {array}c&\underline{Amount}&\underline{\%}&\underline{Amount * \%=Interest\ earned}\\ 4\%\ Interest&x&0.04&0.04x\\\underline{5\%\ Interest}&\underline{4000-x}&\underline{0.05}&\underline{0.05(4000-x)}\\ \quad Total&4000&* * &0.04x+0.05(4000-x)\\\end{array} \\\\\\\underline{\text{Interest earned is given as \$175}}\\0.04x+0.05(4000-x)=175\\0.04x+200-0.05x=175\\200-0.01x=175\\-0.01x=-25\\x=2500\\\\\text{5\% Interest:}\ 4000-x \rightarrow 4000-2500=1500`