Tag: business mathematics and statistics

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Questions Related to business mathematics and statistics

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

Suppose you deposit $ \$900$ per month into an account that pays $4.8 \%$ interest, compounded monthly. How much money will you have after $9$ months? 

  1. $ $8432.97$
  2. $ $1372.44$
  3. $ $9812.97$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $P=\$900,\,R=4.8\%$ and $T=9$ months $=\dfrac{3}{4}$ year

$\Rightarrow$ $A=P\left (1+\dfrac{R}{100}\right)^{4T}$
$\Rightarrow$ $A=900\times \left (1+\dfrac{4.8}{100}\right)^{4\times \frac{3}{4}}$
$\Rightarrow$ $A=900\times \left (\dfrac{131}{125}\right)^3=900\times 1.1510$
$\Rightarrow$ $A=\$1035.9$

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

Identify the correct term for the following definition: It is any asset donated to and for the perpetual benefit of a non-profit institution. The donation is usually made with the requirement that the principal remain intact and money earned from investing the principal be used for a specific purpose.

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

"It is any asset donated to and fro for the perpetual benefit of a non-profit institution. The donation is usually made with the requirement that the principal remain intact and money earned from investing the principal be used for a specific purpose".

Correct term for he above defination is the Endowment.

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

Identify the correct term for the following definition: It is a part of a bond indenture or preferred stock charter that requires the issuer to regularly set money aside in a separate custodial account for the exclusive purpose of redeeming the bonds or shares.

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

"It is a part of a bond indenture or preferred stock charter that requires the issuer to regularly set money aside in a separate custodial account for the exclusive purpose of redeeming the bonds or shares." The correct term for these definition is $\text{Sinking fund}$.

A sinking fund is an account that is used to deposit and save money to repay a debt or replace a wasting asset in the future. 
In other words, it’s like a savings account that you deposit money in regularly and can only be used for a set purpose.
Private and public corporations often use these funds for bonds.

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

What is true about deferred annuity ?

  1. It is an annuity in which the first payment is postponed for period of times.

  2. It is annuity when payments are made at the end of each payment.

  3. It is annuity when payments are made at the beginning of each payment.

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Deferred payment annuities typically offer tax-deferred growth at a fixed or variable rate of return, just like regular annuities. Often deferred payment annuities are purchased for under-age children, with the benefit payments postponed until they reach a certain age. Deferred payment annuities can be helpful in retirement planning.
Option (A) is correct

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

What is true about deferred annuity ?

  1. It is an annuity when the payments are made at the end of payment period.

  2. It is an annuity when the payments are made at the beginning of payment period.

  3. It is an annuity when the payments are made at the middle of payment period.

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  True statement about deferred annuity is,

$-\,It\,is\,an\,annuity\,when\,the\,payment\,are\,made\,at\,the\,end\,of\,payment\,period.$
$\Rightarrow$  A deferred annuity is an insurance contract designed for long-term savings. 
$\Rightarrow$  Unlike an immediate annuity, which starts annual or monthly payments almost immediately, investors can delay payments from a deferred annuity indefinitely. During that time, any earnings in the account are tax-deferred.

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

Which of the following is correct regarding endowment?

  1. Endowments are given to non-profit organizations with the intention that they be used to advance the mission of the organization for the long term.

  2. Endowments of large institutions, sometimes become significant players in the financial world due to the significant amount of money that the endowment is investing.

  3. Both are correct

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$A$ and $B$ both are correct statements regarding endowment which are:

Endowments are given to non-profit organizations with the intention that they be used to advance the mission of the organization for the long term.
Endowments of large institutions, sometimes become significant players in the financial world due to the significant amount of money that the endowment is investing.

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

What amount should be set aside at the end of each year to amount Rs 10 lakhs at the end of 15 years at 6% per annum compound interest?

  1. $5298994$
  2. $3297000$
  3. $4297994$

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$A=10,00,000, t=15,r=6\%$

$A=\sum _{ n=1 }^{ 14 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n }+P } $
$\implies 10,00,000=P[\sum _{ n=1 }^{ 14 }{ { (1+\cfrac { 6 }{ 100 } ) }^{ n }+ 1} ]$
$\implies 10,00,000\times (22.276+1)\ \implies P=Rs.42963$

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

Find the amount of annuity of Rs. 4,000 per annum for 10 years reckoning interest at 10% p.a.
[Given : $(1.1)^{10} = 2.594$]

  1. Rs. 63,760

  2. Rs. 63,670

  3. Rs. 63,205

  4. None.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.4000$

$n=10$
$x=10$%
    $=\dfrac { 10 }{ 100 } =0.1$
$M=\dfrac { P }{ r } \left( { \left( 1+r \right)  }^{ n }-1 \right) $
     $=\dfrac { 4000 }{ 0.1 } \left( { \left( 1.1 \right)  }^{ 10 }-1 \right) $
     $=40000(2.594-1)$
     $=63760$.
$\therefore $  Amount of annuity $=63760$

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

The present value of an annuity of Rs. $3,000$ for $15$ years at $4.5\%$ p.a. CI is?

  1. Rs. $23,809.41$
  2. Rs. $32,218.63$
  3. Rs. $32,908.41$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Payment $P=3000$

$n=15$ years
rate=$4.5%$
$\therefore r=\cfrac { 4.5 }{ 100 } \ =0.045\ PV=P\left( \cfrac { 1-(1+r)^{ -n } }{ r }  \right) \ =3000(\cfrac { 1-(1+(1+0.045)^{ -15 } }{ 0.045 } )\ =3000(\cfrac { 1-(1.045)^{ -15 } }{ 0.045 } )\ =32218.63$
 $\therefore PV$ of the annuity is 
 $32218.63.$