Question

a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in cash management fund paying 9%. after 1 year, the total interest on the two investments is $2,200. how much is invested at each rate

Answer 1

Amount invested at 7% = 16000

Amount invested at 9% = 12000

Explanation:

Let x be the amount invested at 7% and y be the amount invested at 9%.

Since the total amount invested is $28000, therefore, we can set up the first equation as:

`x+y=28000`

Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:

`0.07x+0.09y=2200`

Now we need to solve these two equations to get the values of x and y.

First of all, we multiply the second equation with 100 in order to get rid of decimal values.

`(0.07x+0.09y)*100=2200*100\\7x+9y=220000`

Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.

`y=28000-x`

`7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000`

Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.