Question

How can $42,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?

a) $18,000 at 4%, $24,000 at 10%
b) $24,000 at 4%, $18,000 at 10%
c) $20,000 at 4%, $22,000 at 10%
d) $22,000 at 4%, $20,000 at 10%

Answer 1

To find the amounts to be invested at 4% and 10% annual simple interest such that the interest earned by the two accounts is equal, we can set up and solve a system of equations. The amounts to be invested are $22,000 at 4% and $20,000 at 10%.

Step-by-step explanation:

To find the amount of money to be invested, we can set up an equation using the formula for simple interest: I = P * R * T, where I is the interest, P is the principal (or the amount invested), R is the interest rate, and T is the time in years. Let's call the amount invested at 4% x and the amount invested at 10% y. We can set up the equation:

0.04 * x = 0.10 * y

Since the total amount invested is $42,000, we also have:

x + y = 42,000

Solving this system of equations, we find that x = $22,000 and y = $20,000. Therefore, the answer is (d) $22,000 at 4%, $20,000 at 10%.