You plan to invest $10,000 in two funds paying 4.5% and 5% simple interest. (There is more risk in the 5% fund.) Your goal is to obtain a total annual interest income of $480 from the investments. What is the smallest amount you can invest in the 5% fund and still meet your objective?

$6000

Step-by-step explanation:

Given the following :

Total planned amount to invest = 10,000 in two funds:

Fund A at rates 4.5% and

Fund B at 5% simple interest

Total Annual Interest should be = 480

What is the smallest amount you can invest in the 5% fund and still meet your objective?

Let ;

Investment in fund A = principal = a at 4.5%(0.045)

Investment in fund B = principal = (10000 - a) at 5%(0.05)

Simple interest = principal * rate * time

a + (10000 - a) = 10000

(a * 0.045) + (10000 - a) * 0.05 = 480

0.045a + 500 - 0.05a = 480

-0.005a = 480 - 500

-0.005a = - 20

a = 20 / 0.005

a = 4000

4000 at 4.5%

Investment in fund B = principal = (10000 - a)

(10,000 - 4000) = 6000