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

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

  1. Daughter's Marriage Loan

  2. Life Insurance Plans

  3. Mortgage

  4. All of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

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

  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] $
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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

  1. Contingent Annuity

  2. Deferred Annuity

  3. Perpetual Annuity

  4. Annuity certain
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  1. Rs. 11,260

  2. Rs. 12,160

  3. Rs. 13,200

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

Formula for calculating the amount of an annuity,


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

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

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

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

$F = 12,160$


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

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]

  1. 12 years

  2. 11 years

  3. 13 years

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