An actor invests some money at 6% and $29000 dollars more than 4 times the amount at 9%. The total annual interest earned form the investment is $29910 how much did he invest at each amount
If x at 6%, then
.06x + .09(4x+29000) = 29910
To find out how much the actor invested at each interest rate, let's assume he invested x dollars at 6% and 4 times that amount plus $29000 at 9%.
1. Amount invested at 6%: x
2. Amount invested at 9%: 4x + $29000
Now, let's calculate the annual interest earned from these investments:
Interest earned from the 6% investment: 0.06x (6% written as a decimal)
Interest earned from the 9% investment: 0.09(4x + $29000) (9% written as a decimal)
Given that the total annual interest earned from the investments is $29910, we can set up the equation:
0.06x + 0.09(4x + $29000) = $29910
Now we can solve the equation to find the value of x:
0.06x + 0.36x + $2610 = $29910
0.42x + $2610 = $29910
0.42x = $29910 - $2610
0.42x = $27300
x = $27300 / 0.42
x ≈ $65000
Therefore, the actor invested approximately $65000 at 6% and 4 times that amount plus $29000 at 9%.
Amount invested at 6%: $65000
Amount invested at 9%: 4($65000) + $29000 = $271000 + $29000 = $300000