#### 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

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## Solutions for Chapter 2.2: Insurance and Annuity

Below listed, you can find solutions for Chapter 2.2 of Maharashtra State Board SCERT Maharashtra Question Bank for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022.

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.2 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 2.2 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 2.2 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 2.2 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 0.75%. 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]

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2.2 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`

## Solutions for Chapter 2.2: Insurance and Annuity

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.2 - Insurance and Annuity

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2.2 Insurance and Annuity are Concept of Insurance, Fire Insurance, Accident Insurance, Marine Insurance, Annuity.

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