Actuary

That's where Actuaries come in, as experts who measure and manage risk, making profitable decisions.

Risk is the chance that an undesirable event will occur, but risk is also an opportunity. ​

It’s your turn to be the actuary and try your hand at forecasting the future by solving a problem.

SCL is an insurance company. They've reached out to you to provide your actuarial services, for their new insurance plan for the auto-drivers.

Multiple Choice

SCL insures 2,000 auto drivers. Based on the last 5 year’s data, we know that:

500 of the 2,000 have accidents within a year.

Q: What is the probability of an accident for an auto-rickshaw driver?

Please note: Click on the image to zoom in.

• 0.15

• 0.25

• 1

• 4

The probability of an accident for an auto-rickshaw driver is 0.25.

Calculation:

​Probability of an accident for an auto-rickshaw driver=

• The number of drivers that have an accident within a year ÷ Total number of drivers.

• Thus, P=500÷2000=0.25​

Multiple Choice

Q: How many accidents can you expect to happen each year for the 2000 insured drivers when the probability of an accident is 0.25?

• 0.25

• 4

• 500

• 2000

The company expects 500 accidents each year.

Calculation:

• No. of accidents per year= probability of occurrence of ​an accident × Total no. of drivers insured.

• Thus, ​No. of accidents per year = 0.25 ×2000=500

Multiple Choice

Q: How much money does the company need for the expected number of accidents assuming each accident costs Rs. 20,000?

• ₹6,25,000

• ₹ 12,50,000

• ₹ 1,00,00,000

• ₹1,50,00,000

SCL needs ₹ 1,00,00,000 for the expected number of accident.

Calculation:

• ​Amount needed for the expected no. of accidents= Total no. of expected accidents per year × Amount spent per accident.

• Amount=​ 500×20,000= ​₹ 1,00,00,000

Multiple Choice

If the company needs ₹ 1 crore to cover 500 expected accidents per year, then to make 0 profits how much premium (i.e. annual insurance fee) should the company charge 2000 drivers?

• ₹5,000

• ₹6,250

• ₹20,000

• ₹25,000

To make 0 profits, SCL should charge ₹ 5,000 from each driver.

Calculations:

• The premium for each driver @0 profit= ​Total amount needed for the expected no. of accidents ÷ Total no. of drivers insured

• Thus, Premium= ​₹ 1,00,00,000 ÷ 2000 = ₹ 5,000

Multiple Choice

Q5: If SCL wants to make a profit of 10% (i.e. ₹ 10 Lacs), how much should they charge each driver?

• ₹5,000

• ₹5,500

• ₹25,000

• ₹50,500

To make a 10% profit, SCL should charge ₹ 5,500 from each driver.

Calculations:

• The premium for each driver @10% profit= (​Total amount needed for the expected no. of accidents+ 10% profit of the amount total amount)÷ Total no. of drivers insured

• Thus, Premium= ​(₹ 1,00,00,000+₹ 10,00,000) ÷ 2000 = ₹ 5,500

Multiple Choice

You were advising the SCL for a year and in reality, they got claims from 700 drivers. If SCL had to pay ₹ 20,000 to these drivers, how much total claim amount was paid by SCL?

• ₹1,00,00,000

• ₹1,04,00,000

• ₹1,40,00,000

• ₹1,50,00,000

Total amount paid by SCL would be ₹ 1,40,00,000.

Calculations:

• Total Amount paid for the 700 accidents by SCL = Total no. of accidents per year × Amount spent per accident.

• Total Amount paid by SCL =​ 700×20,000 = ​₹ 1,40,00,000

Multiple Choice

What would be the total profit/loss for SCL in this scenario if they took ₹ 5,500 as a premium from the 2000 auto drivers?

• Profit of ₹30 Lacs

• Loss of ₹30 Lacs

• Loss of ₹40 Lacs

• Neither profit nor loss

SCL had to bear a loss of ₹ 30 Lacs.

Calculations:

• Profit or Loss bourn by SCL = Total premium collected-Total claim amount paid.

  = ₹​1,10,00,000-₹​1, 40,00,000= -₹​30,00,000.

• Thus, SCL would bear a loss of ₹​30,00,000.

Multiple Choice

Next year, SCL wants to make sure it doesn’t run into losses even if 700 drivers file for a claim, what should be its premium for each driver?

• ₹5,500

• ₹7,000

• ₹7,500

• ₹5,000

To avoid any loss, SCL should charge ₹ 7,000 from each driver.

Calculations:

• The premium for each driver= ​Total amount needed for the expected no. of accidents (now 700) ÷ Total no. of drivers insured

• Thus, Premium= ​₹ 1,40,00,000 ÷ 2000 = ₹ 7,000

• ​To understand the trends a little better refer to the table below.

​Total no. of claims	​Premium for each driver	Profit Percentage	​Loss Percentage
​500	₹ 5,000	​0%	​0%
​500	​₹ 5,500	​10%	​0%
​700	​₹ 5,500	​0%	​27.27%
​700	​₹ 7,000	​0%	​0%

Well done!

You did a great job for SCL. They have been running successfully without making any loss, all because of your hard work.

Keep it up!​

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Poll

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