How can $60,000 be invested, part at 7% annual simple interest and the remainder at 12% annual simple interest, so that the interest earned by the two accounts will be equal?
amount invested at 7% ---- x
amount invested at 12% ---- 60000-x
when is
.07x = .12(6000-x) ?
7x = 12(6000-x)
19x = 72000
x = 3789.47
invest $3789.47 at 7% and $5621.05 at 12%
To determine how much of the $60,000 should be invested at each interest rate, we need to set up an equation based on the interest earned by each account.
Let's assume a portion of the $60,000 is invested at 7% annual interest rate. The remaining amount will then be invested at 12% annual interest rate.
Let's denote the amount invested at 7% as "x" and the amount invested at 12% as "y". Since the total investment is $60,000, we have the equation:
x + y = $60,000 [Equation 1]
The interest earned by the amount invested at 7% can be calculated using the formula: Interest = Principal * Rate * Time. In this case, the interest earned is equal to the principal invested (x) multiplied by the interest rate (7%) multiplied by the time (1 year). Therefore, the interest earned on the amount invested at 7% is:
0.07x
Similarly, the interest earned by the amount invested at 12% is:
0.12y
Since we want the interest earned by the two accounts to be equal, we can set up another equation:
0.07x = 0.12y [Equation 2]
Now, we have a system of equations (Equation 1 and Equation 2) that can be solved to determine the values of x and y.
There are multiple ways to solve this system of equations. One approach is to use substitution:
1. Solve Equation 1 for x in terms of y:
x = $60,000 - y
2. Substitute the value of x in Equation 2:
0.07($60,000 - y) = 0.12y
3. Simplify and solve for y:
4,200 - 0.07y = 0.12y
Combine like terms:
4,200 = 0.19y
Divide both sides by 0.19:
y = 4,200 / 0.19
Calculate y:
y = $22,105.26
4. Substitute the value of y in Equation 1 to find x:
x + $22,105.26 = $60,000
Subtract $22,105.26 from both sides:
x = $60,000 - $22,105.26
Calculate x:
x = $37,894.74
Therefore, to earn equal interest on the two accounts, $37,894.74 should be invested at 7% simple interest, and the remaining $22,105.26 should be invested at 12% simple interest.