Phyllis invested 67000 dollars, split between two different accounts. The money in the first account earns simple interest at the rate of 4 percent per year. The money in the second account earns simple interest at the rate of 6 percent per year. After one year the total interest earned on these investments was 3440 dollars. How much money did she invest at each rate?
.04 x + .06 ( 67000-x) = 3440
To solve this problem, we can use a system of equations.
Let's assume Phyllis invested x dollars in the first account and (67000 - x) dollars in the second account.
The amount of interest earned from the first account can be calculated using the formula: interest = principal * rate * time
The interest earned from the second account can be calculated in the same way.
For the first account:
Interest from the first account = x * 0.04 * 1
For the second account:
Interest from the second account = (67000 - x) * 0.06 * 1
According to the given information, the total interest earned was $3440, so we can set up the equation:
Interest from the first account + Interest from the second account = Total interest
x * 0.04 * 1 + (67000 - x) * 0.06 * 1 = 3440
Simplifying the equation:
0.04x + 0.06(67000 - x) = 3440
0.04x + 4020 - 0.06x = 3440
-0.02x = 3440 - 4020
-0.02x = -580
x = -580 / (-0.02)
x = 29000
Phyllis invested $29,000 at a 4% interest rate in the first account. To find out how much she invested at a 6% interest rate in the second account, we subtract the amount invested in the first account from the total investment:
Total investment - Amount invested in the first account = Amount invested in the second account
67000 - 29000 = 38000
Phyllis invested $29,000 at a 4% interest rate in the first account and $38,000 at a 6% interest rate in the second account.