Can someone help me explain this case please

[bombers408]

Credit card

credit limit 5000
account balance 2000
Interest rate(customer) 16%
cost per card 40
annual fee 20
interest rate(C1) 6%
defalult rate 2%

calculate profit per customer! This part I got it

[20-40+2000*(16%-6%)]-5000*2%
=180-100
=80

if credit limit drop from 5000 to 3000

1>other things been equal, what will the profit change

This part I got too
80＋(5000-3000)*2%=80+40=120



How do you get this???
2>if profitable stay the same,
1. how much can account balance change
120-80=(A/B-A'/B'-(16%-6%)
A/B CHANGE=400

Why??
2. how many customer may leave
120N'=80N
N'=2/3N




Q4 how do you calculate the minimum account balance before this new stategy stops being profitable?
I believe we need to calculate the break even point? how do you calculate

 

[Ishuda]

The equation for profit P is
P = ac+B i1 - L i2
where
ac = annual fee - cost per card (anualized) = -20
i1 = Customer interest rate - Business cost interest rate = 10%
i2 = Default interest rate = 2%
B = Balance carried by customer
L = Card limit
So, for
1. how much can account balance change
we want P to be non-negative
ac + B i1 - L i2 > 0 or
B > (L i2 - ac) / i1

For
2. how many customer may leave
what changes other than the number of customers?

 

[bombers408]

The equation for profit P is
P = ac+B i1 - L i2
where
ac = annual fee - cost per card (anualized) = -20
i1 = Customer interest rate - Business cost interest rate = 10%
i2 = Default interest rate = 2%
B = Balance carried by customer
L = Card limit
So, for
1. how much can account balance change
we want P to be non-negative
ac + B i1 - L i2 > 0 or
B > (L i2 - ac) / i1

For
2. how many customer may leave
what changes other than the number of customers?

thanks,
ya how do u solve question 2,3,4