Question

Two investments totaling 38,500 produce an annual income of 2590. One investment yields 3 % per year and while the other yields 10 % per year. How much is invested in each rate ?

Answer 1

Explanation:

Let's assume the amount invested at 3% per year is x dollars.

According to the given information, the amount invested at 10% per year would then be (38500 - x) dollars.

The annual income from the 3% investment would be 0.03x dollars, and the annual income from the 10% investment would be 0.10(38500 - x) dollars.

Given that the total annual income is 2590 dollars, we can set up the equation:

0.03x + 0.10(38500 - x) = 2590

Simplifying the equation, we get:

0.03x + 3850 - 0.10x = 2590

Combining like terms, we have:

-0.07x + 3850 = 2590

Subtracting 3850 from both sides, we get:

-0.07x = -1260

Dividing both sides by -0.07, we get:

x = -1260 / -0.07

x = 18000

Therefore, $18,000 is invested at a 3% rate, and $20,500 (38500 - 18000) is invested at a 10% rate.

Answer 2

The amount invested at 3% per year is $18,000.

The amount invested at 10% per year is $20,500.

Explanation:

Let x be the amount invested that yields 3% per year.

Since the total investment is $38,500, the amount invested that yields 10% per year is (38500 - x).

The annual income from each investment is the product of the amount invested and its percentage yield (in decimal form). Therefore:

The expression for the annual income from the 3% investment is:

`x \cdot 3\%=x \cdot 0.03=0.03x`

The expression for the annual income from the 10% investment is:

`(38500-x) \cdot 10\%=(38500-x) \cdot 0.10=0.1(38500-x)`

We are told that the total annual income from the two investments is $2,590. Therefore, to find the value of x, set the sum of the annual income from each investment to 2590 and solve for x:

`\begin{aligned}0.03x+0.1(38500-x)&=2590\\0.03x+3850-0.1x&=2590\\-0.07x+3850&=2590\\1260&=0.07x\\x&=18000\end{aligned}`

The amount invested at 3% is x, so:

• The amount invested at 3% per year is $18,000.

The amount invested at 10% is (38500 - x), so:

• The amount invested at 10% per year is $20,500.