Question

Shawn has $\$15,000$to invest. She will put some of it into a fund that pays $4.5\%$annual interest and the rest in a certificate of deposit that pays $1.8\%$annual interest. How much should she invest in each account if she wants to earn $4.05\%$ annual interest on the total amount?

Short answer

Shawn has to invest $\$12500$in funds to get annual interest and $\$2500$in the deposit that pays annual interest.

Step-by-step solution

Step 1. Given Information   

The investment made by Shawn is $\$15000$and she will put some of it into a fund that pays $4.5\%$annul interest and the rest in a certificate of deposit that pays $1.8\%$annual interest. We have to find annual interest on the total amount if she wants to earn$4.05\%.$

Step 2. Translate into an equation  

Let xbe the fund she gets by $4.5\%$annual interest.

Now, she invest $\$15000$

So, the deposit she gets by $1.8\%$annual interest is $15000-x$

She wants to earn $4.05\%$annual interest on the total amount.

The equation will be $4.5\left(x\right)+1.8\left(15000-x\right)=4.05\left(15000\right)$

Step 3. Solve the equation 

By proceeding with the equation we get,

$$\begin{gathered} 4.5\left(x\right)+1.8\left(15000-x\right)=4.05\left(15000\right) \\ 4.5x+27000-1.8x=60750 \\ 2.7x=33750 \\ x=12500 \end{gathered}$$

Thus, she has to invest $\$12500$in funds to get $4.5\%$annual interest and $15000-12500=2500$in the deposit that pays$1.8\%$annual interest.

Step 4. Check the answer 

To check the answer replace xby $12500$into the original equation.

$$\begin{gathered} 4.5\left(12500\right)+1.8\left(15000-12500\right)=4.05\left(15000\right) \\ 56250+27000-22500=60750 \\ 60750=60750 \end{gathered}$$

It is true.

Therefore, she should invest $\$12500$in funds and$\$2500$in deposits.