An inheritance of $19,000 was divided among three investments yielding a total of $1490 in simple interest per year. The interest rates for the three investments were 5%, 7%, and 10%. The 5% and 7% investments were $4000 and $1000 less than the 10% investment, respectively. Find the amount placed in each investment.
let the 10% investment be x
then the 5% investment was x - 4000
and the 7% investment was x - 1000
.1x + .05(x-4000) + .07(x - 1000) = 1490
.1x + .05x - 200 + .07x - 70 = 1490
.22x = 1760
x = 8000
The investments were $8000, $4000, and $7000 for the 10%, 5%, and 7% respectively.
To find the amount placed in each investment, we can create a system of equations based on the information given.
Let:
x = amount placed in the 10% investment
x - $4000 = amount placed in the 5% investment
x - $1000 = amount placed in the 7% investment
Now, we can use the formula for simple interest to set up the equations:
0.05(x - $4000) + 0.07(x - $1000) + 0.10x = $1490
Simplifying and solving this equation will give us the value of x, which represents the amount placed in the 10% investment.
Let's solve the equation step by step:
0.05(x - $4000) + 0.07(x - $1000) + 0.10x = $1490
Simplify:
0.05x - $200 + 0.07x - $70 + 0.10x = $1490
Combine like terms:
0.22x - $270 = $1490
Add $270 to both sides:
0.22x = $1760
Divide both sides by 0.22:
x = $1760 / 0.22
x ≈ $8000
Now that we have found the value of x, we can substitute it back into the equations we set up earlier to determine the values of the other investments:
Amount in 10% investment: x ≈ $8000
Amount in 5% investment: x - $4000 ≈ $4000
Amount in 7% investment: x - $1000 ≈ $7000
Therefore, the amounts placed in each investment are approximately $8000, $4000, and $7000, respectively.