Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

Which of the following is not an example of annuity contingent ?

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

  1. Daughter's Marriage Loan

  2. Life Insurance Plans

  3. Mortgage

  4. All of the above

Show answer
Correct Option: C
Explanation:
$\Rightarrow$  $Mortgage$ is not 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.
$\Rightarrow$  Daughter's Marriage loan and Life insurance plans are examples of annuity contingent.

The Future amount of annuity, $(M)$, can be found by

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

  1. $ M=\dfrac{A}{r} \times \left[(1+r)^{n}+1\right] $

  2. $ M=\dfrac{r}{A} \times \left[(1+r)^{n}-1\right] $

  3. $ M=\dfrac{A}{r} \times \left[(1+r)^{n}-1\right] $

  4. $ M=\dfrac{r}{A} \times \left[(1+r)^{n}+1\right] $

Show answer
Correct Option: C
Explanation:

The future amount of annuity (M) can be founded by the formula

$M=\dfrac { A }{ r } \times \left[ { \left( 1+r \right)  }^{ n }-1 \right] $
Where $A$ is amount and $r$ is rate and $n$ is duration

An annuity left unpaid for a certain number of years is called ________ for that number of years.

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

  1. Deferred Annuity

  2. Uniform Annuity

  3. Forborne Annuity

  4. Immediate Annuity

Show answer
Correct Option: C
Explanation:

An annuity left unpaid for a certain number of years is called forborne annuity for that number of years.

If the periodic payments are made at the end of each period, the annuity is called:

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

  1. Annuity due

  2. An immediate annuity

  3. Ordinary annuity

  4. (B) or (C)

Show answer
Correct Option: D
Explanation:

If the periodic payments are made at the end of each period, the annuity is called an immediate annuity or ordinary annuity.

If the period payments start only after a certain specified period it is called.

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

  1. Contingent Annuity

  2. Deferred Annuity

  3. Perpetual Annuity

  4. Annuity certain

Show answer
Correct Option: B
Explanation:

If the period payments start only after a certain specified period it is called deferred annuity.

An annuity whose payments continue till the happening of an event, the date of which cannot be foretold is called.

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

  1. Contingent Annuity

  2. Deferred Annuity

  3. Perpetual Annuity

  4. Annuity certain

Show answer
Correct Option: A
Explanation:

An annuity whose payments continue till the happening of an event, the date of which cannot be foretold is called contingent annuity.

Find the amount of an annuity of Rs. 400 per quarter payable for 6 years at 8% p.a.
[Given : $(1.02)^{24} = 1.608$]-

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

  1. Rs. 11,260

  2. Rs. 12,160

  3. Rs. 13,200

  4. None.

Show answer
Correct Option: B
Explanation:

Formula for calculating the amount of an annuity,


$F=R \dfrac{\left ( 1+\dfrac{r}{m} \right )^{m \times n} -1}{\dfrac{r}{m}}$

$F=400 \dfrac{\left ( 1+\dfrac{8/100}{4} \right )^{4 \times 6} -1}{\dfrac{8/100}{4}}$

$F=400 \dfrac{\left ( 1+\dfrac{8}{100} \times \dfrac{1}{4} \right )^{24} -1}{\dfrac{8}{100} \times \dfrac{1}{4} }$

$F=400 \dfrac{(1.02)^{24} -1}{\dfrac{1}{50} }$

$F = 12,160$


Find the least number of years for which an annuity of Rs. 1,000 must run in order that its amount exceed Rs. 16,000 at 5% p.a. compounded monthly.
[Given : Log 18 = 1.2553, log 105 = 2.8212]

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

  1. 12 years

  2. 11 years

  3. 13 years

  4. None.

Show answer
Correct Option: C
Explanation:
$F=R \dfrac{\left ( 1+\dfrac{r}{m} \right )^{m \times n} -1}{\dfrac{r}{m}}$

$16000=1000 \dfrac{\left ( 1+\dfrac{5}{100} \right )^n -1}{\dfrac{5}{100}}$

$16=1 \dfrac{\left ( 1+\dfrac{5}{100}  \right )^n -1}{\dfrac{5}{100}  }$

$0.8=(1.05)^n-1$

$1.8=(1.05)^n$

Applying log on both sides, we get,

$\log 1.8 = n \log 1.05$

$\Rightarrow n=13$

Least number of years = $13$ years

If the periodic payments are all equal, the annuity is called level of.

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

  1. Deferred Annuity

  2. Uniform Annuity

  3. Forborne Annuity

  4. Immediate Annuity

Show answer
Correct Option: B
Explanation:

If the periodic payments are all equal, the annuity is called level of uniform annuity.

Annuity payable for a fixed number of intervals is called.

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

  1. Contingent Annuity

  2. Deferred Annuity

  3. Perpetual Annuity

  4. Annuity certain

Show answer
Correct Option: D
Explanation:

Annuity payable for a fixed number of intervals is called annuity certain.