Question

Paul has $30000 to invest. His intent is to earn 10% interest on his investment. He can invest part of his money at 6% interest and part at 13% interest. How much does Paul need to invest in each option to make get a total 10% return on his $30000?

Investing for 6% return: $
.
Investing for 13% return: $

Thanks a ton! :)

Answer 1

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86

Explanation:

Let

x ----> the amount invested at 6%

30,000-x -----> the amount invested at 13%

we know that

The interest earned by the amount invested at 6% plus the interest earned by the amount at 13% must be equal to the interest earned by the total amount of $30,000 at 10%

Remember that

`6\%=6\100=0.06`

`13\%=13\100=0.13`

`10\%=10\100=0.10`

so

The linear equation that represent this situation is

`0.06x+(30,000-x)0.13=0.10(30,000)`

solve for x

`0.06x+3,900-0.13x=3,000\\0.13x-0.06x=3,900-3,000\\0.07x=900\\x=\$12,857.14$`

`x-\$30,000=\$17,142.86`

therefore

The amount invested at 6% is $12,857.14

The amount invested at 13% is $17,142.86