Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

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? 

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

  1. $ $8432.97$

  2. $ $1372.44$

  3. $ $9812.97$

  4. None of these

Show answer
Correct Option: D
Explanation:

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

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

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.

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

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these

Show answer
Correct Option: C
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.

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.

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

  1. Scholarship fund

  2. Sinking fund

  3. Endowment

  4. None of these

Show answer
Correct Option: B
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.

What is true about deferred annuity ?

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

  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

Show answer
Correct Option: A
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

What is true about deferred annuity ?

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

  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

Show answer
Correct Option: A
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.

Which of the following is correct regarding endowment?

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

  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

Show answer
Correct Option: C
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.

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?

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

  1. $5298994$

  2. $3297000$

  3. $4297994$

  4. None of the above

Show answer
Correct Option: D
Explanation:

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

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

Find the amount of annuity of Rs. $4000$ p.a. for $10$ years reckoning compound interest at $10\%$ p.a.

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

  1. Rs. $63,706$

  2. Rs. $63,670$

  3. Rs. $67,360$

  4. Rs. $63,760$

Show answer
Correct Option: D
Explanation:
$Payment  \space  'P'= 4000$
$N=10$
$R=10%=10/100=0.1$
$A=P(\dfrac{(1+r)^n - 1)}{r}) $
$=4000(\dfrac{(1.1)^{10} -1}{0.1})$
$=63760$

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

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

  1. Rs. 63,760

  2. Rs. 63,670

  3. Rs. 63,205

  4. None.

Show answer
Correct Option: A
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 $=63760$

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

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

  1. Rs. $23,809.41$

  2. Rs. $32,218.63$

  3. Rs. $32,908.41$

  4. None of the above

Show answer
Correct Option: B,D
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 
 $32218.63.$