StudyRaah StudyRaah XI-XIIOpen StudyRaah

Maharashtra State Board · HSC Commerce · Class 12 (Std XII)

Class 12 Maths and Statistics Part 2 Chapter 2: Insurance and Annuity

Short notes, key concepts, quick revision and practice MCQs with answers

Insurance protects against financial loss from uncertain events, and an annuity is a series of equal payments at regular intervals. The chapter covers premiums, claims under partial insurance, agent's commission, and the accumulated and present values of immediate annuities and annuities due.

Key concepts: Insurance and Annuity

Insurance
A contract in which the insurer agrees to compensate the insured for loss from a specified risk in return for a premium. The document is the policy; the amount covered is the insured value (sum insured).
Types of insurance
Life insurance, and general insurance such as fire, marine (ships and cargo), health, motor and property insurance.
Premium and commission
Premium is paid on the insured value (a rate per cent or per thousand). An insurance agent's commission is paid on the premium.
Claim
If property is insured for less than its value, the claim for a loss is (policy value/property value) × loss.
Annuity
A series of equal payments C made at equal intervals, e.g. EMIs, pensions, recurring deposits. The receiver is the annuitant. i = r/100 is the rate per period and n the number of payments.
Immediate (ordinary) annuity
Payments at the end of each period. Accumulated value A = C[(1 + i)ⁿ − 1]/i. Present value P = C[1 − (1 + i)⁻ⁿ]/i.
Annuity due
Payments at the beginning of each period. A′ = C(1 + i)[(1 + i)ⁿ − 1]/i and P′ = C(1 + i)[1 − (1 + i)⁻ⁿ]/i.
Relations
A = P(1 + i)ⁿ and 1/P − 1/A = i/C. A perpetuity continues for ever with present value C/i. A sinking fund is built by regular deposits to repay a debt or replace an asset.

Quick revision: important points

Practice MCQs with answers

  1. Insurance premium is calculated on the:

    1. Property value
    2. Insured value
    3. Loss
    4. Agent's commission
    Show answer

    Answer: B. Insured value
    Premium is a percentage of the sum insured.

  2. An insurance agent's commission is calculated on the:

    1. Insured value
    2. Premium
    3. Claim
    4. Property value
    Show answer

    Answer: B. Premium
    Commission is a percentage of premium collected.

  3. Property worth ₹5,00,000 is insured for ₹4,00,000. A loss of ₹1,00,000 occurs. The claim is:

    1. ₹1,00,000
    2. ₹80,000
    3. ₹4,00,000
    4. ₹1,25,000
    Show answer

    Answer: B. ₹80,000
    (4,00,000/5,00,000) × 1,00,000 = 80,000.

  4. The premium at 0.5% on an insured value of ₹2,00,000 is:

    1. ₹100
    2. ₹1,000
    3. ₹10,000
    4. ₹500
    Show answer

    Answer: B. ₹1,000
    0.5/100 × 200000 = 1000.

  5. In an immediate annuity, payments are made at the:

    1. Beginning of each period
    2. End of each period
    3. Middle of each period
    4. End of the term only
    Show answer

    Answer: B. End of each period
    Also called an ordinary annuity.

All Class 12 Maths and Statistics chapters

Class 12 Maths and Statistics notes: all chapters