Janet invested $6,000, part at 14% and part at 13%. IF the total interest at the end of year is $820, how much did she invest at 14%?
I did this by trial and error. There might be an easir way, but I don't know what it is.
I tried spitting it in half, but 14% of 3000 is 420 and 13% of 3000 is 390 but the total is too low. So I tried 4000 at 14% and 2000 at 13%. That happens to work. Calculate it to be sure! Good Luck!
let the amount invested at 14% be x,
then the amount invested at 13% would be 6000-x
clearly then
0.14x + 0.13(6000-x) = 820
14x + 13(6000-x) = 82000
easy to solve....
To find out how much Janet invested at 14%, we can set up a system of equations based on the information given.
Let's assume that Janet invested x dollars at 14% and (6000 - x) dollars at 13%.
We know that the interest earned from the investment at 14% can be calculated as (x * 0.14) since interest is usually calculated as a percentage of the principal amount.
Similarly, the interest earned from the investment at 13% can be calculated as ((6000 - x) * 0.13).
According to the given information, the total interest earned from both investments is $820. So, we can write the equation:
(x * 0.14) + ((6000 - x) * 0.13) = 820
Now, we can solve this equation to find the value of x, which represents the amount invested at 14%.
Let's simplify the equation:
0.14x + 0.13(6000 - x) = 820
0.14x + 780 - 0.13x = 820
0.01x = 40
x = 40 / 0.01
x = 4000
Therefore, Janet invested $4000 at 14%.