HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Fill in the blank :

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

Fill in the blank :

If payments of an annuity fall due at the end of every period, the series is called annuity __________.

State whether the following is True or False :

Payment of every annuity is called an installment.

State whether the following is True or False:

Annuity certain begins on a fixed date and ends when an event happens.

State whether the following is True or False :

Annuity contingent begins and ends on certain fixed dates.

State whether the following is True or False :

The present value of an annuity is the sum of the present value of all installments.

State whether the following is True or False :

The future value of an annuity is the accumulated values of all installments.

State whether the following is True or False :

Sinking fund is set aside at the beginning of a business.

Solve the following :

A shopkeeper insures his shop and godown valued at ₹5,00,000 and ₹10,00,000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.

Solve the following :

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. [(1.03)²⁰ = 1.8061]

Solve the following :

Find the amount a company should set aside at the end of every year if it wants to buy a machine expected to cost ₹1,00,000 at the end of 4 years and interest rate is 5% p. a. compounded annually. [(1.05)⁴ = 1.21550625]

Solve the following :

Find the least number of years for which an annuity of ₹3,000 per annum must run in order that its amount exceeds ₹60,000 at 10% compounded annually. [(1.1)¹¹ = 2.8531, (1.1)¹² = 3.1384]

Solve the following :

Find the rate of interest compounded annually if an ordinary annuity of ₹20,000 per year amounts to ₹41,000 in 2 years.

Solve the following :

A person purchases a television by paying ₹20,000 in cash and promising to pay ₹1,000 at end of every month for the next 2 years. If money is worth 12% p. a. converted monthly, find the cash price of the television. [(1.01)^–24 = 0.7875]

Solve the following :

Find the present value of an annuity immediate of ₹20,000 per annum for 3 years at 10% p.a. compounded annually. [(1.1)^–3 = 0.7513]

Solve the following :

A man borrowed some money and paid back in 3 equal installments of ₹2,160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also find the total interest charged. [(1.2)³ = 0.5787]

Solve the following :

A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to ₹9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year. [(1.1)⁴ = 1.4641]

Solve the following :

Find the future value after 2 years if an amount of ₹12,000 is invested at the end of every half year at 12% p. a. compounded half yearly. [(1.06)⁴ = 1.2625]

Solve the following :

After how many years would an annuity due of ₹3,000 p.a. accumulated ₹19,324.80 at 20% p. a. compounded yearly? [Given (1.2)⁴ = 2.0736]

Solve the following :

Some machinery is expected to cost 25% more over its present cost of ₹6,96,000 after 20 years. The scrap value of the machinery will realize ₹1,50,000. What amount should be set aside at the end of every year at 5% p.a. compound interest for 20 years to replace the machinery? [Given (1.05)²⁰= 2.653]