An executive invests $26,000, some at 7% and some at 4% annual interest. If he receives an annual return of $1340, how much is invested at each rate?

Answer 1

Here, we have two unknowns. The principal invested at the first rate and the principal invested at the second rate. Since we have two unknowns, we will need to come up with two equations to solve.

The first equation is $26000=x+y because we know how much the executive invested total between the two principals.

The second equation is $27340=x(1+.07)^1+y(1+.04)^1 which we can use because we know the total investment return. We also know that the interest formula is A=P(1+r/n)^(nt) so x(1+.07) represents the return from the principal x invested in the 7% interest and y(1+.04) represents the return from the principal y invested in the 4% interest. We set this equal to 27430 because this is the total principal invested plus the interest earned.

Solving these two equations results in x (principal invested at 7% interest) to be $10000 and y (principle invested at 4% interest) to be $16000.