Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

Find $y$,if cost of living index number is $200$

Group Food Clothing Fuel and lighting House rent Miscellaneous
I $180$ $120$ $160$ $300$ $200$
W $4$ $5$ $3$ $y$ $2$
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. $12$

  2. $6$

  3. $11$

  4. $7$

Show answer
Correct Option: B
Explanation:

Cost of living index number $= \dfrac{\sum I _{i}W _{i}}{\sum W _{i}}$

$\sum I _{i}W _{i} = 2200 + 300y$

$\sum W _{i} = 14 + y$


$\Rightarrow$ Cost of living index number $= \dfrac{2200 + 300y}{14 + y} = 200$

$\Rightarrow 2200 + 300y = 2800 + 200y$

$\therefore y = 6$

Calculate a price index for the following by using price relative method:

Commodity A B C D E
Price in 1991 (in Rs) 20 40 60 80 100
Price in 1992( in Rs) 70 45 70 90 105
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. 152.24

  2. 153.33

  3. 159.33

  4. 161.24

Show answer
Correct Option: C
Explanation:
 $Commodity$ $Price\, in\,1991$$(in\,Rs.)$ $P _0$   $Price\,in\,1992$$(in\,Rs.)$  $P _1$ $Price\, Relative$[$\dfrac{P _1}{P _0}\times 100$ ]
 $A$  $20$  $70$  $350$ 
 $B$  $40$  $45$   $112.5$
 $C$  $60$  $70$  $116.66$
 $D$  $80$  $90$  $112.5$
 $E$  $100$  $105$  $105$
 $Total$      $796.66$

$\Rightarrow$  Price index by using price relative method = $\dfrac{\sum\dfrac{ P _1}{ P _0}\times 100}{N}=\dfrac{796.66}{5}=159.33$

Construct an index for 1998 taking 1997 as base by average of Relatives:

Commodity A B C D E
Price in 1997 5 4 8 11 2
Price in 1998 7 6 9 12 2
business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

  1. 122.32

  2. 126.04

  3. 132.32

  4. 134.45

Show answer
Correct Option: A
Explanation:
 $Commodity$ $Price\,in\,1997$$(in Rs.)\, [P _0]$  $Price\,in\,1998$$(in\,Rs.)\,[P _1]$  $Price\,relative$$\dfrac{P _1}{P _0}\times 100$ 
 $A$ $5$  $7$  $140$ 
$B$  $4$  $6$  $150$ 
$C$  $8$  $9$  $112.5$ 
$D$  $11$  $12$  $109.09$ 
$E$  $2$  $2$  $100$ 
$Total$      $611.59$ 

$\Rightarrow$  $P _{01}=\dfrac{\sum \dfrac{P _1}{P _0}\times 100}{N}=\dfrac{611.59}{5}=122.32$

$\therefore$   Price index for $1998$, takin $1997$ base year is $122.32$

Amount of money today which is equal to series of payments in future

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. nominal value of annuity

    2. sinking value of annuity

    3. present value of annuity

    4. future value of annuity

    Show answer
    Correct Option: A
    Explanation:

    By definition,

    Nominal value of annuity is the amount of money today which is equal to series of payments in future.

    Annuity, where the payments start after specified no. of periods, is known as

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. Immediate Annuity

    2. Deferred annuity

    3. Contingent annuity

    4. Perpetual annuity

    Show answer
    Correct Option: B
    Explanation:

    An annuity which begins payments only after a period is a deferred annuity
    Annuity, where the payments start after specified no. of periods, is known as Deferred annuity.

    Which of the following is an example of annuity contingent ?

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. Car Loan

    2. House Loan

    3. Daughter's Marriage

    4. All of the above

    Show answer
    Correct Option: C
    Explanation:
    $\Rightarrow$  $Daughter's\,\,Marriage$ is an example of annuity contingent. 
    $\Rightarrow$  Annuity contingent is an annuity arrangement in which the beneficiary does not begin receiving payments until a specified event occurs.
     $\Rightarrow$  A contingent annuity may be set up to begin sending payments to a beneficiary upon the death of another individual who wishes to ensure financial stability for the beneficiary, or upon retirement or disablement of the beneficiary.
    $\Rightarrow$  Car loan and House loan is not an example of annuity contingent, it's an example of annuity certain.

    Security payment type in which payments are made at equal intervals of time and every payment amount is same is classified as _______________.

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. fixed interval investment

    2. fixed payment investment

    3. annuity

    4. lump sum amount

    Show answer
    Correct Option: C
    Explanation:

    An annuity is a series of equal payments in equal time periods. Usually, the time period is $1$ year, which is why it is called an annuity, but the time period can be shorter, or even longer. These equal payments are called the periodic rent. The amount of the annuity is the sum of all payments.
    such security payment type in which payments are made at equal intervals of time and every payment amount is same is classified as annuity.

    If payment of security is paid as $ $100$ at end of year for three years, it is an example of

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. fixed payment investment

    2. lump sum amount

    3. fixed interval investment

    4. annuity

    Show answer
    Correct Option: D
    Explanation:

    The amount of the annuity is the sum of all payments.
    such security payment type in which payments are made at equal intervals of time and every payment amount is same is classified as annuity.
    If payment of security is paid as $100 at end of year for three years, it is an example of annuity.

    What is true about Annuity Due ?

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. It is an annuity in which payments are made at the end of each payment period.

    2. It is an annuity in which payments are made at the beginning of each payment period.

    3. It is an annuity in which payments are made in the middle of each payment period.

    4. None of the above

    Show answer
    Correct Option: B
    Explanation:

    $\Rightarrow$   True statement about Annuity Due is,

    $-It\,is\,an\,annuity\,in\,which\,payments\,are\,made\,at\,the\,beginning\,of\,each\,payment\,period.$
    $\Rightarrow$  Annuity due is an annuity whose payment is to be made immediately at the beginning of each period. 
    $\Rightarrow$  A common example of an annuity due payment is rent, as the payment is often required upon the start of a new month as opposed to being collected after the benefit of rent has been received for an entire month.
    $\Rightarrow$  All payments are in the same amount.
    $\Rightarrow$  All payments are made at the same intervals of time

    Which of the following is true about Annuity Contingent ?

    business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

    1. It is made till the happening of an event.

    2. It is made for fixed number of intervals of time.

    3. Loans for home comes under it

    4. All of the above

    Show answer
    Correct Option: A
    Explanation:

    $\Rightarrow$  True statement about Annuity contingent is $It\,is\,made\,till\,the\,happening\,of\,an\,event.$

    $\Rightarrow$  An annuity arrangement in which the beneficiary does not begin receiving payments until a specified event occurs. 
    $\Rightarrow$  A contingent annuity may be set up to begin sending payments to a beneficiary upon the death of another individual who wishes to ensure financial stability for the beneficiary, or upon retirement or disablement of the beneficiary.