Equilibrium Interest Rate?

Question

I need some serious help here, i'm really confused...

I need the equilibrium interest rate I(r)

here is the given information:

Y = C + I + G
Y = 5,000
G = 1,000
T = 1,000
C= 250 + .75(Y - T)
I = 1,000 - 50r

According to my textbook,
Y - C(Y - T) - G = I(r)

so:
5000 - 250 + .75(5000 - 1000) - 1000 = I(r)
=5000 - 250 + 3000 - 1000
=4750 + 2000
=6750

doesn't make sense...

and then i'm not even sure if i have to do this or not but i tried it

set that equal to the given I which is 1000 - 50r

6750 = 1000 - 50r

subtract 1000 =

6750 = -50r

divide by -50

= -135... whats going on here please give me some help...

Answer 1

5000-250-.75(5000-1000)-1000-1000=-50r
r=5

You need to redo your math. Write it out first as symbols then carefully substitute.