Question

A college student wants to invest the $12,000 inheritance he received and use the annual interest earned to pay his tuition cost of $945. The highest rate offered by a bank is 6% annual simple interest. At this rate, he cannot earn the needed $945, so he decided to invest some of the money in a riskier, but more profitable, investment offering a 9% return. How much should he invest at each rate?

Answer 1

Answer: 4500

Explanation:

Let's denote the amount the student invests at the 6% rate as x, and the amount he invests at the 9% rate as y.

We are given the following information:

Amount invested at 6%: x

Amount invested at 9%: y

Total inheritance: $12,000

Tuition cost: $945

The interest earned from the 6% investment can be calculated as 6% of x, which is 0.06x.

The interest earned from the 9% investment can be calculated as 9% of y, which is 0.09y.

Since the combined interest earned from both investments must cover the tuition cost of $945, we can write the following equation:

0.06x + 0.09y = 945

We also know that the total amount invested must be equal to the inheritance amount:

x + y = 12,000

We now have a system of two equations:

0.06x + 0.09y = 945

x + y = 12,000

We can solve this system of equations to find the values of x and y.

One way to solve this system is to multiply the second equation by -0.06 and add it to the first equation, eliminating the x variable:

-0.06(x + y) + 0.06x + 0.09y = -0.06(12,000) + 945

0.03y = -720 + 945

0.03y = 225

y = 225 / 0.03

y = 7500

Substituting the value of y back into the second equation, we can solve for x:

x + 7500 = 12,000

x = 12,000 - 7500

x = 4500

Therefore, the student should invest $4,500 at the 6% rate and $7,500 at the 9% rate in order to cover the tuition cost of $945 using the interest earned from the investments.