Question

Paul has $90,000 to invest. His intent is to earn 15% interest on his investment. He can invest part of his money at 8% interest and part at 16% interest. How much does Paul need to invest in each option to make a total 15% return on his $90,000?

Answer 1

`\text{Let the amount invested at }8\% \text{ interest rate is x}\\ \text{then the amount to be invested at }16\%\text{ would be }(90000-x)\\ \\ \text{he want to earn a total of }15\% \text{ interest on his inestement.}\\ \text{so we will set up the equation as:}\\ \\ \text{Interset earned at }8\% \text{ rate + Interset earned at }16\% \text{ rate }=15\% \text{ of 90000}\\ \\ \text{we know that the interest earned in 1 year is given by, }I=Pr, \text{ where P}`

`\text{is principle amount and r is the interest rate in decimals. so we have}\\ \\ x(0.08)+(90000-x)(0.16)=0.15(90000)\\ \\ \Rightarrow 0.08x+14400-0.16x=13500\\ \\ \Rightarrow -0.08x=13500-14400\\ \\ \Rightarrow -0.08x=-900\\ \\ \Rightarrow x=(-900)/(-0.08)\\ \\ \Rightarrow x=11250\\ \\ \text{Hence the amount invested at }8\% \text{ intereset is }\$11250\\ \\ \text{and amount invested at }16\% \text{ interest is }=90000-11250=\$78750`