#### Online Mock Tests

#### Chapters

Chapter 1.2: Matrices

Chapter 1.3: Differentiation

Chapter 1.4: Applications of Derivatives

Chapter 1.5: Integration

Chapter 1.6: Definite Integration

Chapter 1.7: Application of Definite Integration

Chapter 1.8: Differential Equation and Applications

Chapter 2.1: Commission, Brokerage and Discount

Chapter 2.2: Insurance and Annuity

Chapter 2.3: Linear Regression

Chapter 2.4: Time Series

Chapter 2.5: Index Numbers

Chapter 2.6: Linear Programming

Chapter 2.7: Assignment Problem and Sequencing

Chapter 2.8: Probability Distributions

## Chapter 2: Insurance and Annuity

### 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]

**Multiple choice questions:**

Rental payment for an apartment is an example of ______

Annuity due

Perpetuity

Ordinary annuity

Installment

**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

**Multiple choice questions:**

The amount which can be demanded under the policy is ______

policy value

premium

interest

claim

**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

**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

**Multiple choice questions: **

The period for the fire insurance policy is ______

one year

two years

three years

four years

**Multiple choice questions: **

Premium is paid on ______ value

property

policy

insured

both policy and insured

**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

**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

**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

### 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]

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

Premium is the amount paid to the insurance company every month

True

False

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

An installment of money paid for insurance is called Premium

True

False

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

The value of insured property is called policy value

True

False

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

A sinking fund is a fund established by financial organization

True

False

**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

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

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

True

False

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

Annuity contingent begins and ends on certain fixed dates

True

False

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

An annuity where payments continue forever is called perpetuity

True

False

### 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]

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

### 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]

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 0.075%. 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 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 0.075%. 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 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]

### 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]

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`

## Chapter 2: Insurance and Annuity

## 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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