HSC Commerce (English Medium) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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 ______

State whether the following statement is True or False:

A sinking fund is a fund established by financial organization

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 

State whether the following statement is True or False:

The future value of an annuity is the accumulated values of all instalments

State whether the following statement is True or False:

Annuity contingent begins and ends on certain fixed dates

State whether the following statement is True or False:

An annuity where payments continue forever is called perpetuity

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 ______

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?

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]

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]

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`

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

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

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 ₹). The estimated sales for 1984 (in 1000 ₹) is