Two investments are made totaling $4800. In the first year they yield a total of $412 in simple interest. Part of the money is invested at 8% and the rest at 9%. Find the amount invested at each interest rate.

Question

Two investments are made totaling $4800. In the first year they yield a total of $412 in simple interest. Part of the money is invested at 8% and the rest at 9%. Find the amount invested at each interest rate.

Answer 1

add up the interest gained on each part. Their sum must be the total earned. If $x is at 8%, then that leaves 4800-x at 9%, so

.08x + .09(4800-x) = 412
x = 2000

Answer 2

Let's assume the amount invested at 8% is x dollars.

According to the given information, the amount invested at 9% would be (4800 - x) dollars.

Now, let's calculate the interest earned from the investment at 8% for one year:

Interest at 8% = (x * 8%)
= (x * 0.08)
= 0.08x

Similarly, let's calculate the interest earned from the investment at 9% for one year:

Interest at 9% = ((4800 - x) * 9%)
= ((4800 - x) * 0.09)
= (0.09 * (4800 - x))

According to the given information, the total interest earned after one year from both investments is $412.

0.08x + 0.09 * (4800 - x) = 412

Now, let's solve the equation for x:

0.08x + 432 - 0.09x = 412
-0.01x = -20
x = -20 / -0.01
x = 2000

So, $2000 is invested at 8%.

The amount invested at 9% would be (4800 - 2000) = $2800.

Therefore, $2000 is invested at 8% and $2800 is invested at 9%.

Answer 3

To find the amount invested at each interest rate, we can set up a system of equations using the given information.

Let's assume the amount invested at 8% is x dollars. This means the amount invested at 9% is $(4800 - x).

We know the total interest earned in the first year is $412.

The interest earned from the amount invested at 8% is (x * 8%).
The interest earned from the amount invested at 9% is ((4800 - x) * 9%).

According to the given information, the total interest earned is $412. So we can write the equation:
(x * 8%) + ((4800 - x) * 9%) = $412

To simplify, convert the percentages to decimal form:
(x * 0.08) + ((4800 - x) * 0.09) = $412

Now, we can solve this equation to find x (the amount invested at 8%):
0.08x + (0.09 * 4800) - (0.09x) = $412
0.08x - 0.09x + 432 - 0.09x = $412
-0.1x = $412 - $432
-0.1x = -$20

Divide both sides of the equation by -0.1 to solve for x:
x = (-$20) / (-0.1)
x = $200

Therefore, $200 was invested at 8% and the rest, $4800 - $200 = $4600, was invested at 9%.