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## Chapter 2: Insurance and Annuity

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 2 Insurance and Annuity Exercise 2.1 [Page 20]

Find the premium on a property worth ₹ 25,00,000 at 3% if the property is fully insured

Find the premium on a property worth ₹25,00,000 at 3% if the property is insured for 80% of its value.

A shop is valued at ₹3,60,000 for 75% of its value. If the rate of premium is 0.9%, find the premium paid by the owner of the shop. Also, find the agents commission if the agent gets commission at 15% of the premium.

A person insures his office valued at ₹5,00,000 for 80% of its value. Find the rate of premium if he pays ₹13,000 as premium. Also, find agent’s commission at 11%.

A building is insured for 75% of its value. The annual premium at 0.70 percent amounts to ₹ 2,625. If the building is damaged to the extent of 60% due to fire, how much can be claimed under the policy?

A stock worth ₹7,00,000 was insured for ₹4,50,000. Fire burnt stock worth ₹3,00,000 completely and damaged the remaining stock to the extent of 75 % of its value. What amount can be claimed under the policy?

A cargo of rice was insured at 0.625% to cover 80% of its value. The premium paid was ₹5,250. If the price of rice is ₹21 per kg, find the quantity of rice (in kg) in the cargo.

60,000 articles costing ₹200 per dozen were insured against fire for ₹2,40,000. If 20% of the articles were burnt and 7,200 of the remaining articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.

The rate of premium is 2% and other expenses are 0.075%. 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 property worth ₹4,00,000 is insured with three companies: A, B, and C. The amounts insured with these companies are ₹1,60,000, ₹1,00,000 and ₹1,40,000 respectively. Find the amount recoverable from each company in the event of a loss to the extent of ₹9,000.

A car valued at ₹8,00,000 is insured for ₹5,00,000. The rate of premium is 5% less 20%. How much will the owner bear including the premium if value of the car is reduced to 60 % of its original value.

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 on a policy of ₹ 1,00,000 is ₹ 56 per thousand per annum. A rebate of ₹ 0.75 per thousand is permitted if the premium is paid annually. Find the net amount of premium payable if the policyholder pays the premium annually.

A warehouse valued at ₹ 40,000 contains goods worth ₹ 2,40,000. The warehouse is insured against fire for ₹ 16,000 and the goods to the extent of 90% of their value. Goods worth ₹ 80,000 are completely destroyed, while the remaining goods are destroyed to 80% of their value due to a fire. The damage to the warehouse is to the extent of ₹ 8,000. Find the total amount that can be claimed under the policy.

A person takes a life policy for ₹2,00,000 for a period of 20 years. He pays premium for 10 years during which bonus was declared at an average rate of ₹20 per year per thousand. Find the paid up value of the policy if he discontinues paying premium after 10 years.

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 2 Insurance and Annuity Exercise 2.2 [Pages 27 - 28]

Find the accumulated (future) value of annuity of ₹800 for 3 years at interest rate 8% compounded annually. [Given (1.08)^{3} = 1.2597]

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 accumulated after 2 years if a sum of ₹24,000 is invested every six months at 12% p.a. compounded half yearly. [Given (1.06)^{4} = 1.2625]

Find accumulated value after 1 year of an annuity immediate in which ₹10,000 is invested every quarter at 16% p.a. compounded quarterly. [Given (1.04)^{4} = 1.1699]

Find the present value of an annuity immediate of ₹36,000 p.a. for 3 years at 9% p.a. compounded annually. [Given (1.09)^{−3} = 0.7722]

Find the present value of an ordinary annuity of ₹63,000 p.a. for 4 years at 14% p.a. compounded annually. [Given (1.14)^{−4} = 0.5921]

A lady plans to save for her daughter’s marriage. She wishes to accumulate a sum of ₹4,64,100 at the end of 4 years. What amount should she invest every year if she gets an interest of 10% p.a. compounded annually? [Given (1.1)^{4} = 1.4641]

A person wants to create a fund of ₹6,96,150 after 4 years at the time of his retirement. He decides to invest a fixed amount at the end of every year in a bank that offers him interest of 10% p.a. compounded annually. What amount should he invest every year? [Given (1.1)^{4} = 1.4641]

Find the rate of interest compounded annually if an annuity immediate at ₹20,000 per year amounts to ₹2,60,000 in 3 years.

Find the number of years for which an annuity of ₹500 is paid at the end of every year, if the accumulated amount works out to be ₹1,655 when interest is compounded annually at 10% p.a.

Find the accumulated value of annuity due of ₹1,000 p.a. for 3 years at 10% p.a. compounded annually. [Given (1.1)^{3} = 1.331]

A person plans to put ₹400 at the beginning of each year for 2 years in a deposit that gives interest at 2% p.a. compounded annually. Find the amount that will be accumulated at the end of 2 years.

Find the present value of an annuity due of ₹600 to be paid quarterly at 32% p.a. compounded quarterly. [Given (1.08)^{−4} = 0.7350]

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

For an annuity immediate paid for 3 years with interest compounded at 10% p.a., the present value is ₹24,000. What will be the accumulated value after 3 years? [Given (1.1)^{3} = 1.331]

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]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 2 Insurance and Annuity Miscellaneous Exercise 2 [Pages 29 - 32]

**Choose the correct alternative :**

“A contract that pledges payment of an agreed upon amount to the person (or his/ her nominee) on the happening of an event covered against” is technically known as

Death coverage

Saving for future

Life insurance

Provident fund

**Choose the correct alternative :**

Insurance companies collect a fixed amount from their customers at a fixed interval of time. This amount is called

EMI

Installment

Contribution

Premium

**Choose the correct alternative :**

Following are different types of insurance.

I. Life insurance

II. Health insurance

III. Liability insurance

Only I

Only II

Only III

All the three

**Choose the correct alternative :**

By taking insurance, an individual

Reduces the risk of an accident

Reduces the cost of an accident

Transfers the risk to someone else.

Converts the possibility of large loss to certainty of a small one.

**Choose the correct alternative :**

You get payments of ₹8,000 at the beginning of each year for five years at 6%, what is the value of this annuity?

₹ 34,720

₹ 39,320

₹ 35,720

₹ 40,000

**Choose the correct alternative :**

In an ordinary annuity, payments or receipts occur at

Beginning of each period

End of each period

Mid of each period

Quarterly basis

**Choose the correct alternative :**

Amount of money today which is equal to series of payments in future is called

Normal value of annuity

Sinking value of annuity

Present value of annuity

Future value of annuity

**Choose the correct alternative :**

Rental payment for an apartment is an example of

Annuity due

Perpetuity

Ordinary annuity

Installment

**Choose the correct alternative :**

______ is a series of constant cashflows over a limited period of time.

Perpetuity

Annuity

Present value

Future value

**Choose the correct alternative :**

A retirement annuity is particularly attractive to someone who has

A severe illness

Risk of low longevity

Large family

Chance of high longevity

**Fill in the blank :**

An installment of money paid for insurance is called __________.

**Fill in the blank :**

General insurance covers all risks except __________.

**Fill in the blank :**

The value of insured property is called __________.

**Fill in the blank :**

The proportion of property value to insured value is called __________.

**Fill in the blank :**

The person who receives annuity is called __________.

**Fill in the blank :**

The payment of each single annuity is called __________.

**Fill in the blank :**

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

**Fill in the blank :**

An annuity where payments continue forever is called __________.

**Fill in the blank :**

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

**Fill in the blank :**

If payments of an annuity fall due at the end of every period, the series is called annuity __________.

**State whether the following is True or False :**

General insurance covers life, fire, and theft.

True

False

**State whether the following is True or False :**

The amount of claim cannot exceed the amount of loss.

True

False

**State whether the following is True or False :**

Accident insurance has a period of five years.

True

False

**State whether the following is True or False :**

Premium is the amount paid to the insurance company every month.

True

False

**State whether the following is True or False :**

Payment of every annuity is called an installment.

True

False

**State whether the following is True or False :**

Annuity certain begins on a fixed date and ends when an event happens.

True

False

**State whether the following is True or False :**

Annuity contingent begins and ends on certain fixed dates.

True

False

**State whether the following is True or False :**

The present value of an annuity is the sum of the present value of all installments.

True

False

**State whether the following is True or False :**

The future value of an annuity is the accumulated values of all installments.

True

False

**State whether the following is True or False :**

Sinking fund is set aside at the beginning of a business.

True

False

**Solve the following :**

A house valued at ₹8,00,000 is insured at 75% of its value. If the rate of premium is 0.80 %, find the premium paid by the owner of the house. If agent’s commission is 9% of the premium, find agent’s commission.

**Solve the following :**

A shopkeeper insures his shop and godown valued at ₹5,00,000 and ₹10,00,000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.

**Solve the following :**

A factory building is insured for `(5/6)^"th"` of its value at a rate of premium of 2.50%. If the agent is paid a commission of ₹2,812.50, which is 7.5% of the premium, find the value of the building.

**Solve the following :**

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.

**Solve the following :**

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?

**Solve the following :**

15,000 articles costing ₹200 per dozen were insured against fire for ₹1,00,000. If 20 % of the articles were burnt completely and 2400 of other articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.

**Solve the following :**

For what amount should a cargo worth ₹25,350 be insured so that in the event of total loss, its value as well as the cost of insurance may be recovered when the rate of premium is 2.5 %.

**Solve the following :**

A cargo of grain is insured at `(3/4)`% to cover 70% of its value. ₹1,008 is the amount of premium paid. If the grain is worth ₹12 per kg, how many kg of the grain did the cargo contain?

**Solve the following :**

4,000 bedsheets worth ₹6,40,000 were insured for `(3/7)^"th"` of their value. Some of the bedsheets were damaged in the rainy season and were reduced to 40% of their value. If the amount recovered against damage was ₹32,000, find the number of damaged bedsheets.

**Solve the following :**

A property valued at ₹7,00,000 is insured to the extent of ₹5,60,000 at `(5/8)^"th"` % less 20%. . Calculate the saving made in the premium.Find the amount of loss that the owner must bear, including premium, if the property is damaged to the extent of 40 % of its value.

**Solve the following :**

Stocks in a shop and godown worth ₹75,000 and ₹1,30,000 respectively were insured through an agent who receives 15% of premium as commission. If the shop was insured for 80% and godown for 60% of the value, find the amount of agent’s commission when the premium was 0.80% less 20%. If the entire stock in the shop and 20% stock in the godown is destroyed by fire, find the amount that can be claimed under the policy.

**Solve the following :**

A person holding a life policy of ₹1,20,000 for a term of 25 years wants to discontinue after paying premium for 8 years at the rate of ₹58 per thousand p. a. Find the amount of paid up value he will receive on the policy. Find the amount he will receive if the surrender value granted is 35% of the premiums paid, excluding the first year’s premium.

**Solve the following :**

A godown valued at ₹80,000 contained stock worth ₹4,80,000. Both were insured against fire. Godown for ₹50,000 and stock for 80% of its value. A part of stock worth ₹60,000 was completely destroyed and the rest was reduced to 60% of its value. The amount of damage to the godown is ₹40,000. Find the amount that can be claimed under the policy.

**Solve the following :**

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. [(1.03)^{20} = 1.8061]

**Solve the following :**

Find the amount a company should set aside at the end of every year if it wants to buy a machine expected to cost ₹1,00,000 at the end of 4 years and interest rate is 5% p. a. compounded annually. [(1.05)^{4} = 1.21550625]

**Solve the following :**

Find the least number of years for which an annuity of ₹3,000 per annum must run in order that its amount exceeds ₹60,000 at 10% compounded annually. [(1.1)^{11} = 2.8531, (1.1)^{12} = 3.1384]

**Solve the following :**

Find the rate of interest compounded annually if an ordinary annuity of ₹20,000 per year amounts to ₹41,000 in 2 years.

**Solve the following :**

A person purchases a television by paying ₹20,000 in cash and promising to pay ₹1,000 at end of every month for the next 2 years. If money is worth 12% p. a. converted monthly, find the cash price of the television. [(1.01)^{–24} = 0.7875]

**Solve the following :**

Find the present value of an annuity immediate of ₹20,000 per annum for 3 years at 10% p.a. compounded annually. [(1.1)^{–3} = 0.7513]

**Solve the following :**

A man borrowed some money and paid back in 3 equal installments of ₹2,160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also find the total interest charged. [(1.2)^{3} = 0.5787]

**Solve the following :**

A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [(1.1)^{4} = 1.4641]

**Solve the following :**

Find the future value after 2 years if an amount of ₹12,000 is invested at the end of every half year at 12% p. a. compounded half yearly. [(1.06)^{4} = 1.2625]

**Solve the following :**

After how many years would an annuity due of ₹3,000 p.a. accumulated ₹19,324.80 at 20% p. a. compounded yearly? [Given (1.2)^{4} = 2.0736]

**Solve the following :**

Some machinery is expected to cost 25% more over its present cost of ₹6,96,000 after 20 years. The scrap value of the machinery will realize ₹1,50,000. What amount should be set aside at the end of every year at 5% p.a. compound interest for 20 years to replace the machinery? [Given (1.05)^{20}= 2.653]

## Chapter 2: Insurance and Annuity

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 2 - Insurance and Annuity

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 2 (Insurance and Annuity) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 2 Insurance and Annuity are Concept of Insurance, Fire Insurance, Accident Insurance, Marine Insurance, Annuity.

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