# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Insurance and Annuity [Latest edition]

## Chapter 2: Insurance and Annuity

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Q.1

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Insurance and Annuity Q.1

#### MCQ [1 Mark]

Q.1 | Q 1

Multiple choice questions:

Rental payment for an apartment is an example of ______

• Annuity due

• Perpetuity

• Ordinary annuity

• Installment

Q.1 | Q 2

Multiple choice questions:

In an ordinary annuity, payments or receipts occur at ______

• Beginning of each period

• End of each period

• Mid of each period

• Quarterly basis

Q.1 | Q 3

Multiple choice questions:

The amount which can be demanded under the policy is ______

• policy value

• interest

• claim

Q.1 | Q 4

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 ______

• 6,400

• 6,000

• 6,450

• 6,500

Q.1 | Q 5

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 ______

• ₹ 4,400

• ₹ 4,000

• ₹ 5,000

• ₹ 5,500

Q.1 | Q 6

Multiple choice questions:

The period for the fire insurance policy is ______

• one year

• two years

• three years

• four years

Q.1 | Q 7

Multiple choice questions:

Premium is paid on ______  value

• property

• policy

• insured

• both policy and insured

Q.1 | Q 8

Multiple choice questions:

In annuity calculations, the interest is usually taken as ______

• simple interest per annum

• interest compounded every year

• interest compounded per month

• simple interest per month

Q.1 | Q 9

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 ______

• ₹ 4,000

• ₹ 4,500

• ₹ 3,500

• ₹ 4,200

Q.1 | Q 10

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 ______

• 40,000

• 36,300

• 36,286.75

• 36289.25

Q.2

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Insurance and Annuity Q.2

#### [1 Mark]

Q.2 | Q 1

State whether the following statement is True or False:

Premium is the amount paid to the insurance company every month

• True

• False

Q.2 | Q 2

State whether the following statement is True or False:

An installment of money paid for insurance is called Premium

• True

• False

Q.2 | Q 3

State whether the following statement is True or False:

The value of insured property is called policy value

• True

• False

Q.2 | Q 4

State whether the following statement is True or False:

A sinking fund is a fund established by financial organization

• True

• False

Q.2 | Q 5

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

• True

• False

Q.2 | Q 6

State whether the following statement is True or False:

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

• True

• False

Q.2 | Q 7

State whether the following statement is True or False:

Annuity contingent begins and ends on certain fixed dates

• True

• False

Q.2 | Q 8

State whether the following statement is True or False:

An annuity where payments continue forever is called perpetuity

• True

• False

Q.3

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Insurance and Annuity Q.3

#### Fill in the blanks: [1 Mark]

Q.3 | Q 1

In ordinary annuity, payments or receipts occur at ______

Q.3 | Q 2

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 ₹ ______

Q.3 | Q 3

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 ______

Q.3 | Q 4

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

Q.3 | Q 5

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

Q.3 | Q 6

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

Q.3 | Q 7

______ insurance is not covered by general insurance

Q.4

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Insurance and Annuity Q.4

#### Questions; [3 Marks]

Q.4 | Q 1

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%

Q.4 | Q 2

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.

Q.4 | Q 3

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

Q.4 | Q 4

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.

Q.4 | Q 5

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?

Q.4 | Q 6

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]

Q.4 | Q 7

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]

Q.4 | Q 8

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

Q.4 | Q 9

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]

Q.4 | Q 10

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]

Q.5

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Insurance and Annuity Q.5

#### Activity based Question [4 Marks]

Q.5 | Q 1. 1)

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

Q.5 | Q 1. ii)

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

Q.5 | Q 2

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

Q.5 | Q 3

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

Q.5 | Q 4

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

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## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Insurance and Annuity

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 Insurance and Annuity are Concept of Insurance, Fire Insurance, Accident Insurance, Marine Insurance, Annuity.

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