Tag: insurance and annuity

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

Present value of annuity, $(V)$, can be found by

  1. $ V=\dfrac{r}{A} \times \left[1-(1+r)^{(-n)}\right] $
  2. $ V=\dfrac{A}{r} \times \left[1-(1+r)^{(-n)}\right] $
  3. $ V=\dfrac{A}{r} \times \left[1-(1+r)^{(n)}\right] $
  4. $ V=\dfrac{r}{A} \times \left[1-(1+r)^{(n)}\right] $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The present value annuity factor is used for simplifying the process of calculating the present value of an annuity. A table is used to find the present value per dollar of cash flows based on the number of periods and rate per period. Once the value per dollar of cash flows is found, the actual periodic cash flows can be multiplied by the per dollar amount to find the present value of the annuity.
$v= \frac{A}{r} \times [1-(1+r)^{(-n)}]$
where , A =annuity , r =rate per period , n= number of periods

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

Annuity where payments are made at the end of each payment period, i.e. 1st payment is made at the end of the 1st payment interval, and so on, is known as 

  1. Perpetual annuity

  2. Contingent annuity

  3. Ordinary annuity

  4. Immediate annuity
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

Answer is Ordinary or Immediate Annuity.

  1. An ordinary annuity or immediate annuity is where payments are made at the end of each payment period, i.e. 1st payment is made at the end of the 1st payment interval, and so on. Examples are repayment of car loans, house mortgage etc.
  2. A contingent annuity is one where the term depends upon some event whose occurrence is not fixed. An example is periodic payments of life insurance premiums which stop when the person dies.
  3. A perpetual annuity is an annuity whose term does not end, i.e. it extends till infinity. Thus there is no last payment; they go on forever. An example is freehold property, where you can earn rent in perpetuity.