Tag: financial mathematics

Questions Related to financial mathematics

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 
 $32218.63.$

Rs. $200$ is invested at the end of each month in an account paying interest $6\%$ per year compounded monthly. What is the future value of this annuity after $10$th payment? Given that $(1.005)^{10}=1.0511$.

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

  1. $2,044$

  2. $2,404$

  3. $2,440$

  4. $2,004$

Show answer
Correct Option: A
Explanation:

A$=$Rs. $200$
$n=10$
i$=6\%$ p.a. $=6/12\%$ per month $=0.005$
Future value of annuity after $10$ months is given by
A(n, i)$=A\left[\displaystyle\frac{(1+i)^n-1}{i}\right]$
$A(10, 0.005)=200\left[\displaystyle\frac{(1+0.005)^{10}-1}{0.005}\right]$
$=$Rs. $2,044$.

Belose Infrastructures  just issued 10 million Rs100-par bonds payable carrying 8% coupon rate and maturing in 5 years. The bond indenture requires GI to set up a sinking up to pay off the bond at the maturity date. Semi-annual payments are to be made to the fund which is expected to earn 10% per annum. Find the amount of required periodic contributions.

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

  1. 7905155

  2. 7950515

  3. 8950515

  4. 6950515

Show answer
Correct Option: B

An annuity is?

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

  1. A fixed sum

  2. Paid at regular intervals

  3. Under certain stated conditions

  4. All of the above

Show answer
Correct Option: D
Explanation:

An annuity is 

$(1)$A fixed sum
$(2)$ Paid at regular intervals
$(3)$Under certain stated conditions.