Mixed problems

Question

Stephanie inherited $40,000. She wants to put some of the money in a certificate of deposit that pays 2.1% interest per year and the rest in a mutual fund account that pays 6.5% per year. How much should she invest in each account  she wants to earn 5.4% interest per year on the total amount? 

Answer 1

Yesenia,

 

Our strategy here is going to be to use systems of equations to solve this problem. Let x represent the amount of money invested in the 2.1% account and y represent the amount of money invested in the 6.5% account. Since we have a total of 40,000 dollars to invest, we get this equation:

 

x + y = 40,000

 

Now let's remind ourselves how annual interest works. If I invest x dollars into an account with 2.1% annual interest, the amount of money gained at the end of the year would be 0.021x.  In other words, to find the amount of money we would gain from interest, we convert the interest percentage into a decimal and then multiply it by the amount we invested. So the total amount of money we would make in a year from investing in these two accounts will be 0.021x + 0.065y

 

Additionally, we want our aggregated interest rate to be 5.4%. So our total interest gained will be equal to 0.054 x 40,000=2,160. And so we get this equation:

 

0.021x + 0.065y = 2160

 

Now we have two equations with the variables x and y. So we can set up a system of equations to find x and y.

 

0.021x + 0.065y = 2160

     x    +    y      = 40000

 

I think you should be able to take it from here. I hope it helps.