An executive invests $26,000, some at 7% and some at 5% annual interest. If he receives an annual return of $1580, how much is invested at each rate?

Question

how do i figure this out

Answer 1

If he invests 100% of the $26,000 then the percentage of it invested at 7% and the percentage invested at 5% must sum to 100%.

 

So let's set the percentage of the amount invested at 7% equal to x. The amount invested at 5% must be equal to 1-x in order for them to sum to 100%.

 

Now let's find out what rate of return he received:  1580/26000 = 6.07%

 

Because the investors return is a weighted average of 5% and 7% we can create this equation:

 

5%(1-x) + 7%(x) = 6.07%

 

5% - 5%(x) + 7%(x) = 6.07%

 

2%(x) = 1.07%

 

x= .535 or 53.5% or $13,910

 

The investor invested $13,910 at 7% and $12,090 at 5%.