Question

Marco has$\$8,000$to save for his daughter’s college education. He wants to divide it between one account that pays $3.2\%$interest per year and another account that pays $8\%$ interest per year. How much should he invest in each account if he wants the interest on the total investment to be $6.5\%$?

Short answer

Marco invested$\$2500at3.2\%and\$5500at8\%.$

Step-by-step solution

Step 1. Given information

Two banks of different interest rates are given.

One bank gives$3.2\%$interest per year and the other bank gives$8\%$interest per year.

Step 2. Equation formation

The total interest on total amount$=6.5\%$

If $x$amount is invest in one bank for interest of $3.2\%=0.032$, then$8000-x$will be invested in the other with$8\%=0.08$

Therefore, the equation will become,

$0.032\left(x\right)+0.08(8000-x)=0.065\left(8000\right)$

Step 3. Solution of the equation

The equation is:

$$\begin{gathered} 0.032\left(x\right)+0.08(8000-x)=0.065\left(8000\right) \\ 0.032x+640-0.08x=520 \\ -0.048x=540-640 \\ 0.048x=120 \\ x=2500 \\ 8000-x=8000-2500 \\ =5500 \end{gathered}$$