An actor invested some money at 9% simple interest, and $30,000 more than four times the amount at 12%. The total annual interest earned from the investment was $38.370. How much did the actor invest at each amount?
$____ at 9%
$____ at 12%
Assuming a typo in the interest amount,
.09x + .12(30000+4x) = 38370
I think I solved it...
.09(61000)+.12(274000) = $38,370
so...
$61k at 9%
$274k at 12%
Feel free to comment as I am bad at explaining how I came up with these numbers.
To solve this problem, we can set up two equations based on the information given:
Let's say the amount invested at 9% is "x" dollars.
The amount invested at 12% would then be "4x + $30,000" (four times the amount at 9%, plus $30,000).
The first equation represents the interest earned from the 9% investment:
0.09x (9% as a decimal) = interest earned at 9%
The second equation represents the interest earned from the 12% investment:
0.12(4x + $30,000) (12% as a decimal) = interest earned at 12%
We also know that the total annual interest earned from both investments is $38,370:
0.09x + 0.12(4x + $30,000) = $38,370
Now, let's solve the equation to find the value of "x" (the amount invested at 9%):
0.09x + 0.12(4x + $30,000) = $38,370
0.09x + 0.48x + $3,600 = $38,370
0.57x + $3,600 = $38,370
0.57x = $38,370 - $3,600
0.57x = $34,770
x = $34,770 / 0.57
x ≈ $61,052
Therefore, the actor invested approximately $61,052 at 9% and approximately $244,208 ($61,052 * 4 + $30,000) at 12%.