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

## Chapter 2: Insurance and Annuity

Exercise 2.1Exercise 2.2Miscellaneous Exercise 2
Exercise 2.1 [Page 20]

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

Exercise 2.1 | Q 1.1 | Page 20

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

Exercise 2.1 | Q 1.2 | Page 20

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

Exercise 2.1 | Q 2 | Page 20

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.

Exercise 2.1 | Q 3 | Page 20

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%.

Exercise 2.1 | Q 4 | Page 20

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?

Exercise 2.1 | Q 5 | Page 20

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?

Exercise 2.1 | Q 6 | Page 20

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.

Exercise 2.1 | Q 7 | Page 20

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.

Exercise 2.1 | Q 8 | Page 20

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.

Exercise 2.1 | Q 9 | Page 20

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.

Exercise 2.1 | Q 10 | Page 20

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.

Exercise 2.1 | Q 11 | Page 20

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%.

Exercise 2.1 | Q 12 | Page 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.

Exercise 2.1 | Q 13 | Page 20

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.

Exercise 2.1 | Q 14 | Page 20

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.

Exercise 2.2 [Pages 27 - 28]

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

Exercise 2.2 | Q 1.01 | Page 27

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

Exercise 2.2 | Q 1.02 | Page 27

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]

Exercise 2.2 | Q 1.03 | Page 27

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]

Exercise 2.2 | Q 1.04 | Page 27

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]

Exercise 2.2 | Q 1.05 | Page 27

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]

Exercise 2.2 | Q 1.06 | Page 27

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]

Exercise 2.2 | Q 1.07 | Page 28

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]

Exercise 2.2 | Q 1.08 | Page 28

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]

Exercise 2.2 | Q 1.09 | Page 28

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

Exercise 2.2 | Q 1.1 | Page 28

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.

Exercise 2.2 | Q 1.11 | Page 28

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]

Exercise 2.2 | Q 1.12 | Page 28

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.

Exercise 2.2 | Q 1.13 | Page 28

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]

Exercise 2.2 | Q 1.14 | Page 28

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

Exercise 2.2 | Q 1.15 | Page 28

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]

Exercise 2.2 | Q 1.16 | Page 28

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]

Miscellaneous Exercise 2 [Pages 29 - 32]

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

Miscellaneous Exercise 2 | Q 1.01 | Page 29

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

Miscellaneous Exercise 2 | Q 1.02 | Page 29

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

Miscellaneous Exercise 2 | Q 1.03 | Page 29

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

Miscellaneous Exercise 2 | Q 1.04 | Page 29

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.

Miscellaneous Exercise 2 | Q 1.05 | Page 29

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

Miscellaneous Exercise 2 | Q 1.06 | Page 29

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

Miscellaneous Exercise 2 | Q 1.07 | Page 29

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

Miscellaneous Exercise 2 | Q 1.08 | Page 29

Choose the correct alternative :

Rental payment for an apartment is an example of

• Annuity due

• Perpetuity

• Ordinary annuity

• Installment

Miscellaneous Exercise 2 | Q 1.09 | Page 29

Choose the correct alternative :

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

• Perpetuity

• Annuity

• Present value

• Future value

Miscellaneous Exercise 2 | Q 1.1 | Page 29

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

Miscellaneous Exercise 2 | Q 2.01 | Page 29

Fill in the blank :

An installment of money paid for insurance is called __________.

Miscellaneous Exercise 2 | Q 2.02 | Page 29

Fill in the blank :

General insurance covers all risks except __________.

Miscellaneous Exercise 2 | Q 2.03 | Page 29

Fill in the blank :

The value of insured property is called __________.

Miscellaneous Exercise 2 | Q 2.04 | Page 29

Fill in the blank :

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

Miscellaneous Exercise 2 | Q 2.05 | Page 29

Fill in the blank :

The person who receives annuity is called __________.

Miscellaneous Exercise 2 | Q 2.06 | Page 29

Fill in the blank :

The payment of each single annuity is called __________.

Miscellaneous Exercise 2 | Q 2.07 | Page 29

Fill in the blank :

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

Miscellaneous Exercise 2 | Q 2.08 | Page 29

Fill in the blank :

An annuity where payments continue forever is called __________.

Miscellaneous Exercise 2 | Q 2.09 | Page 30

Fill in the blank :

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

Miscellaneous Exercise 2 | Q 2.1 | Page 30

Fill in the blank :

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

Miscellaneous Exercise 2 | Q 3.01 | Page 30

State whether the following is True or False :

General insurance covers life, fire, and theft.

• True

• False

Miscellaneous Exercise 2 | Q 3.02 | Page 30

State whether the following is True or False :

The amount of claim cannot exceed the amount of loss.

• True

• False

Miscellaneous Exercise 2 | Q 3.03 | Page 30

State whether the following is True or False :

Accident insurance has a period of five years.

• True

• False

Miscellaneous Exercise 2 | Q 3.04 | Page 30

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 2 | Q 3.05 | Page 30

State whether the following is True or False :

Payment of every annuity is called an installment.

• True

• False

Miscellaneous Exercise 2 | Q 3.06 | Page 30

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 2 | Q 3.07 | Page 30

State whether the following is True or False :

Annuity contingent begins and ends on certain fixed dates.

• True

• False

Miscellaneous Exercise 2 | Q 3.08 | Page 30

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

Miscellaneous Exercise 2 | Q 3.09 | Page 30

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 2 | Q 3.1 | Page 30

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 2 | Q 4.01 | Page 30

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.

Miscellaneous Exercise 2 | Q 4.02 | Page 30

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.

Miscellaneous Exercise 2 | Q 4.03 | Page 30

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.

Miscellaneous Exercise 2 | Q 4.04 | Page 30

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.

Miscellaneous Exercise 2 | Q 4.05 | Page 30

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?

Miscellaneous Exercise 2 | Q 4.06 | Page 30

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.

Miscellaneous Exercise 2 | Q 4.07 | Page 30

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 %.

Miscellaneous Exercise 2 | Q 4.08 | Page 30

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?

Miscellaneous Exercise 2 | Q 4.09 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.1 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.11 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.12 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.13 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.14 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.15 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.16 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.17 | Page 31

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.

Miscellaneous Exercise 2 | Q 4.18 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.19 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.2 | Page 31

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]

Miscellaneous Exercise 2 | Q 4.21 | Page 32

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]

Miscellaneous Exercise 2 | Q 4.22 | Page 32

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]

Miscellaneous Exercise 2 | Q 4.23 | Page 32

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]

Miscellaneous Exercise 2 | Q 4.24 | Page 32

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

Exercise 2.1Exercise 2.2Miscellaneous Exercise 2

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

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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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