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Mathematics and Statistics · Class 12 Commerce

Ch 10Insurance and Annuity — Class 12 Mathematics and Statistics, concept-first.

This Maharashtra Std XII (Commerce) Mathematics and Statistics chapter joins two everyday tools of financial planning — insurance, which protects against loss, and annuity, which turns a lump sum into (or builds a lump sum from) a stream of equal payments.

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Key concepts

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Fire and Property Insurance (Average Clause)

When a property is insured for less than its full value, the average clause makes the policyholder bear a proportionate share of any loss: , capped at the sum insured and at the actual loss.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Insurance — Meaning and Basic Terms

This Maharashtra Std XII (Commerce) Mathematics and Statistics chapter joins two everyday tools of financial planning — insurance, which protects against loss, and annuity, which turns a lump sum into…

2

Types of Insurance — Life, Fire, Marine and Property

Insurance is classified by what it protects. Std XII focuses on the four common kinds and their premium arithmetic.

3

Premium and Policy Value

Most straightforward insurance problems ask you to move between three quantities: the sum insured, the premium rate, and the premium — given any two, find the third.

4

Fire / Property Insurance and the Average Clause

The average clause is the single most important idea in property and fire insurance. It penalises under-insurance so that a policyholder who insures for less than the full value bears a proportionate…

5

Annuity — Meaning and Types

An annuity is the mathematics of regular equal payments — a recurring deposit, an insurance premium, a loan instalment, a pension.

6

Accumulated (Future) Value of an Annuity

The accumulated value (also called the future value or amount) of an annuity is what the stream of payments grows to, at the moment of the last payment, once each payment has earned compound interest.

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Present Value of an Annuity

The present value of an annuity is the single lump sum today that is financially equivalent to the whole future stream of payments — i.e.

8

Sinking Fund and EMI

Two of the most useful applications of annuities are the sinking fund (saving up for a future lump sum) and the EMI (repaying a loan) — one is an accumulated-value problem solved for , the other a pre…

Exercises

+Show 6 questions6 questions
  1. Q5A shop worth ₹10,00,000 suffers a fire loss of ₹3,00,000. The policy carries an average clause and the claim admitted is ₹1,80,000. Find the…Free
  2. Q6The premium on a marine insurance policy is ₹9,000, charged at a rate of 1.5% of the sum insured. Find the sum insured (policy value).Free
  3. Q10Find the present value of an annuity due of ₹1,000 paid at the beginning of each year for 3 years at 10% per annum. [Given (1.1)^(-3) = 0.75…Preview
  4. Q13A person deposits ₹10,000 at the end of each year for 2 years into a fund earning 5% per annum compounded annually. Find the accumulated val…Preview
  5. Q14For the same periodic payment, rate and number of periods, the present value of an annuity due compared with that of an immediate (ordinary)…Preview
  6. Q15A building worth ₹12,00,000 is insured for ₹9,00,000 under an average-clause policy. Fire damages it to the extent of ₹4,00,000. The claim a…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 10 questions10 questions
  1. Q1A 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 exte…Preview
  2. Q2______ is a series of constant cash flows over a limited period of time. (a) Perpetuity (b) Annuity (c) Present value (d) Future valuePreview
  3. Q3In an ordinary annuity, payments or receipts occur at ______. (a) Beginning of each period (b) End of each period (c) Mid of each period (d)…Preview
  4. Q4A 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…Preview
  5. Q5In an ordinary annuity, payments or receipts occur at ______. (a) Beginning of each period (b) End of each period (c) Mid of each period (d)…Preview
  6. Q6A 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 hous…Preview
  7. Q7Insurance companies collect a fixed amount from their customers at a fixed interval of time. This amount is called ______. (a) EMI (b) Insta…Preview
  8. Q8A 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, fi…Preview
  9. Q9For what amount should a cargo worth ₹25,350 be insured so that in the event of loss, its value as well as cost of insurance may be recovere…Preview
  10. Q10Find the present value of an annuity immediate of ₹18,000 per annum, for 3 years at 9% per annum, compounded annually. [Given: $(1.09)^{-3}…Preview

More questions

+Show 9 questions9 questions
  1. Example 1A factory building is insured against fire for ₹5,00,000. The premium rate is 0.8% of the sum insured. Find the premium payable.Free
  2. Example 2A shopkeeper insures his stock worth ₹1,50,000 for 80% of its value. If the premium rate is 2%, find (i) the sum insured and (ii) the premiu…Free
  3. Example 3A godown valued at ₹8,00,000 is insured for ₹6,00,000. A fire causes damage worth ₹2,00,000. The policy has an average clause. Find the amou…Free
  4. Example 4A property worth ₹4,00,000 is insured for its full value of ₹4,00,000 under a policy with an average clause. A fire causes a loss of ₹1,00,0…Preview
  5. Example 7A person deposits ₹2,000 at the end of each year for 3 years into an account paying 10% per annum compounded annually. Find the accumulated…Preview
  6. Example 8Find the accumulated value of an annuity due of ₹5,000 paid at the beginning of each year for 3 years at 10% per annum compounded annually.…Preview
  7. Example 9Find the present value of an immediate annuity of ₹1,000 paid at the end of each year for 3 years at 10% per annum. [Given (1.1)^(-3) = 0.75…Preview
  8. Example 11A company sets up a sinking fund to accumulate ₹1,00,000 in 4 years to replace a machine, by depositing an equal amount at the end of each y…Preview
  9. Example 12A loan of ₹50,000 is to be repaid in 3 equal annual instalments at 10% per annum. Find the annual instalment (EMI). [Given (1.1)^3 = 1.331]Preview