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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 
 $32218.63.$

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

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 $(1.005)^{10}=1.0511$.

  1. $2,044$
  2. $2,404$
  3. $2,440$
  4. $2,004$
Reveal answer Fill a bubble to check yourself
A Correct answer
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. $2,044$.

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

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.

  1. 7905155

  2. 7950515

  3. 8950515

  4. 6950515
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a sinking fund problem. The periodic payment is calculated using the formula for an annuity: PMT = FV * i / ((1+i)^n - 1). With semi-annual periods, n=10 and i=0.05.