1. John’s loans for his business total $155,000. One of the loans is a SBA loan at 11% interest; the other loan is a Community Business Partner loan whose interest is 6.5% After one year the loans accumulated $12,325 in interest. What was the amount of each loan?
I am not sure what equation needs to be used for this
Invested $X in SBA.
Invested $Y in CBP.
X + y = $155,000,
Y = 155000 - x.
0.11x + 0.065(155000-x) = 12,325,
0.11x + 10075 - 0.065x = 12,325,
0.045x = 12,325 - 10075 = 2250,
X = $50,000 Invested in SBA.
Y = 155000 - 50000 = $105,000 Invested in CBP.
To solve this problem, we can set up a system of equations using the given information.
Let's assume that the amount of the SBA loan is represented by 'x' and the amount of the Community Business Partner loan is represented by 'y'.
From the problem, we know that:
- The total amount of the loans is $155,000, so we have the equation: x + y = 155,000 (Equation 1)
- The interest on the SBA loan is 11% and the interest on the Community Business Partner loan is 6.5%. After one year, the total interest accumulated is $12,325, so we have the equation: 0.11x + 0.065y = 12,325 (Equation 2)
Now, we have a system of two equations with two variables. We can solve this system using various methods, such as substitution or elimination.
Let's use the elimination method to solve this system.
Multiply Equation 1 by 0.065:
0.065x + 0.065y = 0.065 * 155,000
This simplifies to:
0.065x + 0.065y = 10,075 (Equation 3)
Now, subtract Equation 3 from Equation 2:
(0.11x + 0.065y) - (0.065x + 0.065y) = 12,325 - 10,075
This simplifies to:
0.045x = 2,250
Divide both sides of the equation by 0.045:
x = 2,250 / 0.045
x = $50,000
Now, substitute the value of x back into Equation 1 to find y:
$50,000 + y = $155,000
Subtract $50,000 from both sides of the equation:
y = $155,000 - $50,000
y = $105,000
Therefore, the amount of the SBA loan is $50,000 and the amount of the Community Business Partner loan is $105,000.