Question

An automotive insurance company has 30,000 policyholders, and the accident rate is 0.06.
If the company needs to make a profit of $1,740,000 this year and the payout for each claim (after deductibles) is $8,200, the minimum premium it must charge is $_______.

The company’s financial advisers have predicted that in the upcoming year, the accident rate will increase by 5% of the base rate and the number of policyholders will increase by 12%. If the company’s profit needs and the payout for each claim remain the same, the minimum premium should increase by $_____.

Answer 1

@Preetha @mathmate

Answer 2

First part:-

Profit = income - outgoings

outgoings = 30,000 * 0.06 * 8200 dollars
profit = 1,740,000
income = 30,000 x where x = premium

Answer 3

form an equation and solve for x

Answer 4

550?

Answer 5

yes good job

Answer 6

thanks!

Answer 7

yw
for the second part you need to multiply 0.06 by 1.05 ( = 5*% increase)

Answer 8

and the 30,000 by 1.12 ( = 12% increase)

and do the same calculation

Answer 9

wait would you add them?

Answer 10

no the calculation with the 2 above changes will give a new premium
they want the increase in premium so subtract the iold premium from the new one

Answer 11

33599.937?

Answer 12

what is that figure?

Answer 13

I subtracted the (.06*1.05) from the (30,000*1.12)

Answer 14

did i do it wrong?:(

Answer 15

this is way to work out the new premium


outgoings = 30,000 * 1.12* 0.06 * 1.05 * 8200 dollars
profit = 1740000
income = 30000*1.12* x

x = (174000 + 30,000 * 1.12* 0.06 * 1.05 * 8200 ) / (30,000 * 1.12)

Answer 16

x = 568.39 dollars

so increase = 568.39 - 550

Answer 17

yes that subtraction was wrong

Answer 18

so 18.39 is the answer?

Answer 19

yes

Answer 20

ok thank you!

Answer 21

you have to go back to the original formula with the new amounts

Answer 22

yw