Question

How can $60,000 be​ invested, part at 10% annual simple interest and the remainder at 5% annual simple​ interest, so that the interest earned by the two accounts will be​ equal?

Answer 1

Explanation:

Let's assume that the amount invested at 10% is x, and the amount invested at 5% is (60000 - x), since the total investment is $60,000.

The interest earned on the 10% investment after one year would be 0.10x, and the interest earned on the 5% investment after one year would be 0.05(60000 - x).

We are given that the interest earned by the two accounts is equal, so we can set up an equation:

0.10x = 0.05(60000 - x)

Simplifying this equation, we get:

0.10x = 3000 - 0.05x

Adding 0.05x to both sides, we get:

0.15x = 3000

Dividing both sides by 0.15, we get:

x = 20000

Therefore, the amount invested at 10% is $20,000, and the amount invested at 5% is ($60,000 - $20,000) = $40,000.

To check that the interest earned is equal for both investments, we can calculate:

Interest earned on 10% investment = 0.10($20,000) = $2,000

Interest earned on 5% investment = 0.05($40,000) = $2,000

As expected, the interest earned on both investments is equal.