SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.2 - Insurance and Annuity [Latest edition]

Multiple choice questions:

Rental payment for an apartment is an example of ______

Multiple choice questions:

In an ordinary annuity, payments or receipts occur at ______

Multiple choice questions:

The amount which can be demanded under the policy is ______

Multiple choice questions:

A shop valued ₹ 2,00,000 is insured at 80% of it’s value. If the rate of premium is 4%, then the premium is ______

Multiple choice questions:

If the claim under the policy is ₹ 4,000 and ratio of property value to policy value is 5:4 then loss occurred is ______

Multiple choice questions: 

The period for the fire insurance policy is ______

Multiple choice questions: 

Premium is paid on ______  value

Multiple choice questions:  

In annuity calculations, the interest is usually taken as ______

Multiple choice questions:

If for an immediate annuity r = 10% p.a., P = ₹ 12,679.46 and A = ₹ 18,564, then the amount of each annuity paid is ______

Multiple choice questions:

The present value of an immediate annuity of ₹ 10,000 paid each quarter for four quarters at 16% p.a. compounded quarterly is ______

State whether the following statement is True or False:

Premium is the amount paid to the insurance company every month

State whether the following statement is True or False:

An installment of money paid for insurance is called Premium

State whether the following statement is True or False:

The value of insured property is called policy value

State whether the following statement is True or False:

A sinking fund is a fund established by financial organization

State whether the following statement is True or False:

The relation between accumulated value ‘A’ and present value ‘P’ is A = P(1+ i)ⁿ 

State whether the following statement is True or False:

The future value of an annuity is the accumulated values of all instalments

State whether the following statement is True or False:

Annuity contingent begins and ends on certain fixed dates

State whether the following statement is True or False:

An annuity where payments continue forever is called perpetuity

In ordinary annuity, payments or receipts occur at ______

The present value of an immediate annuity for 4 years at 10% p.a. compounded annually is ₹ 23,400. It’s accumulated value after 4 years would be ₹ ______

If for an immediate annuity r = 10% p.a., P = ₹ 12,679.46 and A = ₹ 18,564, then the amount of each annuity paid is ______

An annuity in which each payment is made at the end of period is called ______

If payments of an annuity fall due at the beginning of every period, the series is called annuity ______

The intervening time between payment of two successive installments is called as ______

______ insurance is not covered by general insurance

A shop and a godown worth ₹ 1,00,000 and ₹ 2,00,000 respectively were insured through an agent who was paid 12% of the total premium. If the shop was insured for 80% and the godown for 60% of their respective values, find the agent's commission, given that the rate of premium was 0.80% less 20%

The rate of premium is 2% and other expenses are 0.75%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.

A merchant takes fire insurance policy to cover 80% of the value of his stock. Stock worth ₹ 80,000 was completely destroyed in a fire. while the rest of stock was reduced to 20% of its value. If the proportional compensation under the policy was ₹ 67,200, find the value of the stock

The rate of premium is 2% and other expenses are 0.75%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.

A 35-year old person takes a policy for ₹ 1,00,000 for a period of 20 years. The rate of premium is ₹ 76 and the average rate of bonus is ₹ 7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?

A person invested ₹ 5,000 every year in finance company that offered him interest compounded at 10% p.a., what is the amount accumulated after 4 years? [Given (1.1)⁴ = 1.4641]

Find the amount of an ordinary annuity if a payment of ₹ 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly. [Given (1.03)²⁰ = 1.8061]

An annuity immediate is to be paid for some years at 12% p.a. The present value of the annuity is ₹ 10,000 and the accumulated value is ₹ 20,000. Find the amount of each annuity payment

A person sets up a sinking fund in order to have ₹ 1,00,000 after 10 years. What amount should be deposited bi-annually in the account that pays him 5% p.a. compounded semi-annually? [Given (1.025)²⁰ = 1.675]

A company decides to set aside a certain sum at the end of each year to create a sinking fund, which should amount to ₹ 4 lakhs in 4 years at 10% p.a. Find the amount to be set aside each year?
[Given (1.1)⁴ = 1.4641]

Property value = ₹ 12,50,000

Rate of premium, r = ₹ 3%

If property is fully insured, the policy value is same as property value therefore policy value = `square`

Premium = `"r"/100 xx "policy value"`

= `square/100 xx 12,50,000`

= `square`

Property value = ₹ 12,50,000

Rate of premium, r = ₹ 3%

If property is 80% insured

Policy value = 80% of its property value

= `square/100 xx 12,50,000`

= ₹ 10,00,000

Premium = `square/100 xx 10,00,000`

= ₹ `square`

Policy value = ₹ 80,000

Period of policy = 20 years

Amount of money paid in 10 years = `square`

Annualized average rate per bonus = ₹ 20 per thousand per year

For one year, bonus = `square/1000 xx 80,000`

= ₹ 1,600

Bonus for 10 years = `10 xx square`

= ₹ 16,000

Total amount after 10 years = `square + 16000`

= ₹ `square`

For annuity due,

C = ₹ 20,000, n = 3, I = 0.1, (1.1)^–3 = 0.7513

Therefore, P = `square/0.1 xx [1 - (1 + 0.1)^square]`

= 2,00,000 [1 – 0.7513]

= ₹ `square`

The future amount, A = ₹ 10,00,000

Period, n = 20, r = 5%, (1.025)²⁰ = 1.675

A = `"C"/"I" [(1 + "i")^"n" - 1]`

I = `5/200` = `square` as interest is calculated semi-annually

A = 10,00,000 = `"C"/"I" [(1 + "i")^"n" - 1]`

10,00,000 = `"C"/0.025 [(1 + 0.025)^square - 1]`

= `"C"/0.025 [1.675 - 1]`

10,00,000 = `("C" xx 0.675)/0.025`

C = ₹ `square`