Question

Suzanne scarpula invested $30,000, part of it in a high risk venture fund that yielded 11.5% per year and the rest In a secure mutual fund paying interest of 6% per year. At the end of one year, Suzanne’s investments earned $2,790. Find the amount she invested at each rate.

Answer 1

$18,000 was invested in the high-risk venture fund and $12,000 was invested in the mutual fund.

Explanation:

In this problem we have two unknowns:
`a` the amount invested in the high-risk venture fund and
`b`, the amount invested in the mutual fund and we know that the sum of
`a` and
`b` is $30,000.

The amount earned ($2,790) can be expressed in the following equation:

`0.115a+0.06b=2790`, where
`a` is multiplied by 11.5% and b is multiplied by 6%

Since we know that the sum of
`a` and
`b` is $30,000, we can rearrange that equation to solve for
`a`, as follows:

`a = 30000-b`

We can now replace
`a` in the earlier equation to obtain an expression with only one unknown value:

`0.115(30000-b) + 0.06b = 2790`

Which can be rearranged and solved for
`b`:

`3450 - 0.115b + 0.06b = 2790\\b = 12000`

Now, using the fact that
`a+b=30000` we can find
`a`:

`a=30000-b=30000-12000=18000`

Therefore, $18,000 must have been invested in the high-risk venture fund at 11.5% and $12,000 in the mutual fund at 6%