HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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]

Use the method of least squares to fit a trend line to the data in Problem 1 above. Also, obtain the trend value for the year 1975.

The following table gives the production of steel (in millions of tonnes) for years 1976 to 1986.

Fit a trend line to the above data by the graphical method.

Choose the correct alternative :

Which of the following can’t be a component of a time series?

Moving averages are useful in identifying ______. 

An overall upward or downward pattern in an annual time series would be contained in which component of the times series?

Choose the correct alternative :

The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year. Y = 500 + 60X (in 1000 Rs). The estimated sales for 1984 (in 1000 Rs) is:

Which component of time series refers to erratic time series movements that follow no recognizable or regular pattern?

Fill in the blank :

_______ component of time series is indicated by a smooth line.

_______ component of time series is indicated by periodic variation year after year.

_______ component of time series is indicated by a long wave spanning two or more years.

Fill in the blank :

_______ component of time series is indicated by up and down movements without any pattern.

State whether the following is True or False :

The secular trend component of time series represents irregular variations.