Question

An investor has $300,000 to invest. If part is invested at 5% and the rest at 9%, how much should be invested at 5% to yield 8% on the total amount?

Answer 1

To achieve an 8% return on a $300,000 investment with parts invested at 5% and 9%, $75,000 should be invested at 5%.

Step-by-step explanation:

To determine how much should be invested at 5% to yield an 8% return on the total amount of $300,000, we can set up a system of equations. Let's call the amount invested at 5% x and the amount invested at 9% y. The total investment is $300,000, so we have:

x + y = $300,000 (Equation 1)

Since we want an 8% yield on the total, the total interest from both investments should be 8% of $300,000, which is $24,000. The interest from the amount x at 5% is 0.05x, and the interest from the amount y at 9% is 0.09y. Therefore, we have:

0.05x + 0.09y = $24,000 (Equation 2)

Now, we will solve Equation 1 for y:

y = $300,000 - x (Equation 3)

Next, we substitute Equation 3 into Equation 2:

0.05x + 0.09($300,000 - x) = $24,000

Solving for x, we get:

0.05x + $27,000 - 0.09x = $24,000

-0.04x = -$3,000

x = $75,000

Therefore, $75,000 should be invested at 5% to yield an 8% return on the total amount.