Chris takes out two loans. He borrows $800 more from a credit union that charges 12% interest than from a bank that charges 15% interest. If his interest payments total $420 annually, how much does he borrow at each rate?
assuming no compunding of interest:
borrow x at .15
borrow (x+800) at .12
then
.15 x + .12 (x+800) = 420
let his loan from the bank be $x
let the loan from the credit union be $(x+800)
.15x + .12(x+800) = 420
solve for x, let me know what you got.
There has to be two equations. I got 1,200 for x...
1200 and 2000 are the correct amounts.
If you really, really, want to make two equations out of this:
x = amount at .15
y = amount at .12
then
.15 x + .12 y = 420
y = x + 800
then substitute equation 2 into equation 1
.15 x + .12(x+800) = 420
which is where we started.
To solve this problem, we can set up a system of equations using the given information. Let's denote the amount borrowed from the bank as 'x' and the amount borrowed from the credit union as 'x + $800'.
We know that the interest rate from the bank is 15%, so the interest paid on that loan will be 0.15x. The interest rate from the credit union is 12%, so the interest paid on that loan will be 0.12(x + $800).
Since his total interest payments are $420 annually, we can set up the equation:
0.15x + 0.12(x + $800) = $420
Now, we can solve this equation to find the values of 'x' (amount borrowed from the bank) and 'x + $800' (amount borrowed from the credit union).
0.15x + 0.12x + 0.12($800) = $420
0.27x + $96 = $420
0.27x = $420 - $96
0.27x = $324
Dividing both sides of the equation by 0.27, we get:
x = $324 / 0.27
x ≈ $1200
So, Chris borrowed approximately $1200 from the bank. To find out how much he borrowed from the credit union, we can substitute this value back into any of the original equations:
Amount borrowed from the credit union = x + $800
≈ $1200 + $800
≈ $2000
Therefore, Chris borrowed $1200 from the bank and $2000 from the credit union.