Question

An inheritance of $100,000 is divided among three investments yielding $8,750 in interest per year. The interest rates of the three investments are 17.5%, 22.5%, and 27.5% simple interest. Find the amount placed in each investment when the second is $7,500 less than the first amount and the third amount is $12,500 less than the first amount. Round all answers to two decimal places when applicable.

Answer 1

Answer: The first investment is $40,000, the second investment is $32,500, and the third investment is $27,500.

Explanation:

To find the amount placed in each investment, we can set up a system of equations based on the given information:

Let x be the amount placed in the first investment.

The second investment is $7,500 less than the first, so the amount in the second investment is x - $7,500.

The third investment is $12,500 less than the first, so the amount in the third investment is x - $12,500.

The total amount invested is $100,000, so we can write the equation:

x + (x - $7,500) + (x - $12,500) = $100,000

Simplifying the equation:

3x - $20,000 = $100,000

Adding $20,000 to both sides:

3x = $120,000

Dividing both sides by 3:

x = $40,000

So, the amount placed in the first investment is $40,000.

The amount placed in the second investment is $40,000 - $7,500 = $32,500.

The amount placed in the third investment is $40,000 - $12,500 = $27,500.

Therefore, the amount placed in each investment is as follows:

First investment: $40,000

Second investment: $32,500

Third investment: $27,500

Remember, we set up a system of equations to find the amounts placed in each investment. By solving the equations, we find that the first investment is $40,000, the second investment is $32,500, and the third investment is $27,500.