John runs a florist shop in a small arkansas town and had to borrow $170,000 to start up the shop. He was able to borrow some from the state business development office at 4% but the rest he had to borrow from a friend who charged him 8%. The first year John paid $9800 in interest. How much did he borrow from his friend?
I = Po*r*t
I = $9800
r = 0.08
t = 1 yr.
Solve Po, the amount borrowed.
To solve this problem, we can set up a system of equations. Let's represent the amount John borrowed from the state business development office as "x" (in dollars) and the amount he borrowed from his friend as "y" (in dollars).
According to the given information, John's total borrowed amount is $170,000:
x + y = 170,000 Equation 1
We are also told that the interest paid in the first year was $9,800. The interest paid for the loan from the state business development office can be calculated by multiplying the borrowed amount (x) by the interest rate (4% = 0.04):
x * 0.04 = interest from state loan Equation 2
The interest paid for the loan from his friend can be calculated by multiplying the borrowed amount (y) by the interest rate (8% = 0.08):
y * 0.08 = interest from friend loan Equation 3
We know that the total interest paid was $9,800:
interest from state loan + interest from friend loan = 9,800
Substituting Equations 2 and 3 into this equation, we have:
x * 0.04 + y * 0.08 = 9,800
Now, we can solve this system of equations (Equations 1 and the updated equation above) to find the values of x and y.
Let's multiply Equation 1 by 0.04 to align the terms:
0.04x + 0.04y = 6,800
Next, combine this equation with the updated equation:
0.04x + 0.04y + 0.08y = 6,800 + 9,800
0.04x + 0.12y = 16,600
Now, substitute the value of 0.04x from Equation 2:
0.04(170,000 - y) + 0.12y = 16,600
Multiply and simplify:
6,800 - 0.04y + 0.12y = 16,600
0.08y = 9,800
y = 9,800 / 0.08
y ≈ 122,500
Therefore, John borrowed approximately $122,500 from his friend.