Lynn wishes to realize a return of 11% on her investments. If she has $10,000 invested at 9%, how much additional money should she invest at 15%?
To find out how much additional money Lynn should invest at 15% in order to realize a return of 11% on her investments, we can use the concept of weighted averages. This involves taking into account the rates of return and the amounts invested at those rates.
Let's break down the problem:
1. Lynn currently has $10,000 invested at a rate of 9%. This means she will earn a return on this investment of 9% of $10,000, which is 0.09 * $10,000 = $900.
2. Lynn wants to realize an overall return of 11%. This means that the total return she wants to earn is 0.11 * (sum of her initial investment + additional investment amount).
3. Let's assume the additional investment amount is x.
Now we can set up an equation to solve for x:
Return from 9% investment + Return from 15% investment = Total desired return
$900 + (0.15 * x) = 0.11 * (10,000 + x)
Simplifying the equation:
900 + 0.15x = 0.11 * (10,000 + x)
900 + 0.15x = 1,100 + 0.11x
0.15x - 0.11x = 1,100 - 900
0.04x = 200
x = 200 / 0.04
x = $5,000
Therefore, Lynn should invest an additional $5,000 at a rate of 15% in order to realize a return of 11% on her investments.