Question

Theodore invests a total of $17,500 in two accounts paying 2% and 12% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $950.00.

Answer 1

11,500 at 2% and $6,000 at 12%.

Explanation:

Let x represent amount invested at 2% and y represent amount invested at 12%.

We have been given that Theodore invests a total of $17,500 in two accounts. We can represent this information in an equation as:

`x+y=17500...(1)`

`x=17500-y...(1)`

We are also told that he invested $17,500 in two accounts paying 2% and 12% annual interest, respectively. After one year, the total interest was $950.00.

Interest earned at 2% in one year would be
`0.02x`.

Interest earned at 12% in one year would be
`0.12y`

`0.02x+0.12y=950...(1)`

Upon substituting equation (1) in equation (2), we will get:

`0.02(17500-y)+0.12y=950`

`350-0.02y+0.12y=950`

`350+0.10y=950`

`350-350+0.10y=950-350`

`0.10y=600`

`(0.10y)/(0.10)=(600)/(0.10)`

`y=6000`

Therefore, Theodore invested $6,000 at 12%.

Upon substituting
`y=6000` in equation (1), we will get:

`x=17500-6000`

`x=11500`

Therefore, Theodore invested $11,500 at 2%.