John invested $2500, part at 8% and the rest at 12% per annum. The two parts earned equal amount of interest in one year. How much was invested at each rate?

Question

John invested $2500, part at 8% and the rest at 12% per annum. The two parts earned equal amount of interest in one year. How much was invested at each rate?

Answer 1

All you have to do is multiply parts of the 2500 by .08 and .12 then find which amount is the same.

EXP 1250 * .08 = 100 1250 * .12 = 150 since those don't match go to 1300*.08 and 1200*.12 and so on untill you find the same answer

Answer 2

Let the amount invested at 8% be x

then the amount invested at 12% is 2500-x

.08x = .12(2500-x)
times a 100
8x = 12(2500-x)
8x = 30000 - 12x
20x = 30000
x = 1500

So John investe $1500 at 8% and $1000 at 12%

Check: .08(1500) = 120 , and .12(1000) = 120

Answer 3

would you really have to multiply .08 and .12 by 100 or could you leave it the way it is?

Answer 4

You could just work with the decimals.

I just like to work with whole numbers rather than decimals or fractions.
That is because calculators did not exist for most of my teaching career and we had to do calculations in our heads or with pencil and paper.

Answer 5

I see well think you for showing me an easier and faster way to figure that problem out. I was taught the long way on most math problems.

Answer 6

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that the amount invested at 8% is x dollars. Therefore, the amount invested at 12% would be (2500 - x) dollars. The interest earned on both investments is equal, so we can equate the interest earned from both investments.

The formula for simple interest is I = P * R * T, where:
- I is the interest earned
- P is the principal (the amount invested)
- R is the interest rate per annum
- T is the time period

Using this formula, we can set up the following equation for the interest earned at 8%:

I = x * (8/100) * 1

And the following equation for the interest earned at 12%:

I = (2500 - x) * (12/100) * 1

Since the interest earned is equal in both cases, we can set these two equations equal to each other:

x * (8/100) * 1 = (2500 - x) * (12/100) * 1

Simplifying this equation, we have:

0.08x = 0.12(2500 - x)

Now let's solve for x:

0.08x = 0.12 * 2500 - 0.12x

0.08x + 0.12x = 0.12 * 2500

0.20x = 0.12 * 2500

x = (0.12 * 2500) / 0.20

x = 1500

So, John invested 1500 dollars at 8% and (2500 - 1500) = 1000 dollars at 12%.