Nick invests a total of $28,000 in two accounts paying 8% and 4% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,780.00.
was invested at 8%
and was invested at 4%
Let x be the amount invested at 8% and y be the amount invested at 4%.
We know that x + y = $28,000. (Equation 1)
We also know that 0.08x + 0.04y = $1,780. (Equation 2)
Simplifying equation 1, we have x = $28,000 - y.
Substituting this into equation 2, we get 0.08($28,000 - y) + 0.04y = $1,780.
Expanding the equation we get, $2,240 - 0.08y + 0.04y = $1,780.
Combining like terms, we have -0.04y = - $460.
Dividing both sides of the equation by -0.04, we get y = $11,500.
Substituting the value of y into equation 1, we get x + $11,500 = $28,000.
Subtracting $11,500 from both sides of the equation, we get x = $16,500.
Therefore, Nick invested $16,500 at 8% and $11,500 at 4%.