Probability? (Checking my work)?

Question

Checking my work on my statistics stuff...

You're an insurance agent, selling insurance: $1000 policies against occurence B. B happens to 2% of the people owning the policy, historically. There's a $20 administrative fee for each policy sold.

How much does each policy have to cost to make a $100 profit on each?

Here's basically what I did:
P=profit, n=number of policies, p=price per policy, P/n=profit per policy

P=np-20n-(1000n*.02)
P=np-40n
P/n=p-40
100=p-40
p=140

Is that about right?

Answer 1

Comes out right, I think, but an algebraic, not statistical way of getting there.

try this:
expected payout per policy = $1,000 * 2%
thats $20
plus costs $20
plus profit $100

comes out at $140

see, just abit more statistical

Answer 2

it is right but unnecessarily complex

cost =Profit +claims+admin charge
for 1000 policy
cost = 100 + .02[1000] + 20 = 140

i.e. it is redundant to include a number n

Answer 3

expected pay-out 2%*1000 = 20
fee $20
so the costs are $40

you want to gain 100 so 140 per insurance.

same as atoa

Answer 4

Works for me.

Answer 5

Your logic seems perfectly sound to me.

Answer 6

You are correct...I got the same result.