Tag: amount of an annuity

Questions Related to amount of an annuity

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)

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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

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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

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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.

An annuity which continues forever(infinite number of years) 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: C
Explanation:

Perpetual annuity is an annuity which continues forever i.e. infinite number of year.

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

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

  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] $

Show answer
Correct Option: B
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

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 

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

  1. Perpetual annuity

  2. Contingent annuity

  3. Ordinary annuity

  4. Immediate annuity

Show answer
Correct Option: C,D
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.