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

A man borrows Rs. $ 30000$ at $12 \%$ per annum compound interest from a bank and promises to pay off the loans in $20$ annual instalments beginning at the end of the first year . What is the annual payment necessary?

  1. $4016.76$
  2. $3013.54$
  3. $4065.24$
  4. $1034.54$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, $V=Rs.30000,\,\,r=12\%=0.12$ and $n=20$.

We know $V=\dfrac{A}{r}[1-(1+r)^{-n}]$
Thus $30000=\dfrac{A}{0.12}[1-(1+0.12)^{-20}]$
$\Rightarrow$   $A=\dfrac{30000\times 0.12}{[1-(1+0.12)^{-20}]}$
$\Rightarrow$  $A=\dfrac{3600}{[1-(1.12)^{-20}]}$
$\Rightarrow$  $A=$ Rs. $4016.76$

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

A person borrowed some money and returned it in 3 equal quarterly instalments of Rs 4630.50 each. What sum (approximately) did he borrow if the rate of interest was 20 % per annum.compounded quarterly?

  1. 12613.48

  2. 10613.48

  3. 11613.48

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  We have $A=Rs.4630.50,\, n=3$ and rate of interest is $20\%$ which is compounded quarterly. So, $r=5\%$

$\Rightarrow$ We have to find sum borrow i.e. $V$
$\Rightarrow$  $V=\dfrac{A}{r}[1-(1+r)^{-n}]$

$\Rightarrow$  $V=\dfrac{4630.50}{0.05}[1-(1+0.05)^{-3}]$  

$\Rightarrow$  $V=\dfrac{463050}{5}[1-(1.05)^{-3}]$

$\Rightarrow$  $V=92610\times \dfrac{1261}{9261}$

$\Rightarrow$  $V=10\times 1261$

$\Rightarrow$  $V=Rs.12610$

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

A person takes a loan on compound interest and returns it in $2$ equal installments . If the rate of interest is $10$% per annum and the yearly installment is Rs $1682$. Find the interest charged with second installment.

  1. Rs.$613.2$
  2. Rs.$603.2$
  3. Rs.$513.2$
  4. Rs.$713.2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=\cfrac{A}{(1+\cfrac{R}{100})^n}$

$\implies \cfrac{1682}{(1+\cfrac{10}{100})^1}$$+\cfrac{1682}{(1+\cfrac{10}{100})^2}$
$ \implies 1592.09+1390.08=2919.17\approx 2920$
$\implies A _2=2920(1+\cfrac{10}{100})^2=3533.2$
$CI=A _1-P=3533.2-2920=Rs.613.2$

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

A person takes a loan on compound interest and returns it in $2$ equal installments . If the rate of interest is $10$% per annum and the yearly installment is Rs $1682$. Find the principal (approximately).

  1. $2920$
  2. $3450$
  3. $2346$
  4. $2275$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=\cfrac{A}{1+(\cfrac{R}{100})^n}$

$\implies \cfrac{1682}{1+(\cfrac{10}{100})^1}$$+\cfrac{1682}{1+(\cfrac{10}{100})^2}$
$ \implies 1592.09+1390.08=2919.17\approx 2920$
$\implies A=Rs.2920$

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

A sinking fund is created for the redemption of debentures of Rs 10,000 at the end of 25 years. How much money should be provided out of profits each year for the sinking fund if the investment can earn interest at the rate 4% per annum?

  1. 2408.19

  2. 1408.19

  3. 3408.19

  4. 5408.19
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using formula of sinking fund

$M=\cfrac{A}{r}[(1+r)^n-1]$
$\implies 1000= \cfrac{A}{0.04}[(1+0.04)^{25}-1]\implies A=2408.19$

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

A person takes a loan on compound interest and returns it in $2$ equal installments . If the rate of interest is $10$% per annum and the yearly installment is Rs $1682$. Find the interest charged (approximately) with first installment.

  1. Rs. $202$
  2. Rs. $192$
  3. Rs. $92$
  4. Rs. $292$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$P=\cfrac{A}{(1+\cfrac{R}{100})^n}$

$\implies \cfrac{1682}{(1+\cfrac{10}{100})^1}$$+\cfrac{1682}{(1+\cfrac{10}{100})^2}$
$ \implies 1592.09+1390.08=2919.17\approx 2920$
$\implies A _1=2920(1+\cfrac{10}{100})=3212$
$CI=A _1-P=3212-2920=Rs.292$

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 certain ?

  1. Car Loan

  2. Daughter's Marriage

  3. House Loan

  4. All of above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\Rightarrow$  $Daughter's\,\,Marriage$ is not an example of annuity certain.
$\Rightarrow$  Annuity certain is annuity that, as a minimum, guarantees a fixed number of payments. It continues over the life of the annuitant, even if he or she lives beyond the number of payments specified in the annuity contract. 
$\Rightarrow$ In case the annuitant dies before exhausting the payments, a named beneficiary continues to receive the remaining number. Also called life annuity certain or life annuity certain and continuous.
$\Rightarrow$  House loan and Car loan are examples of annuity certain.
Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

A man borrowed some money and paid back in 3 equal instalments of Rs 2160 each. What sum did he borrow if the rate of interest charged was 20 % p.a .compounded annually?

  1. 4551.12

  2. 4334.24

  3. 4768.97

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that,

$A=P(1+\cfrac{r}{100})^n$
$\implies 2160=P(1+\cfrac{20}{100})^2\ \implies P=Rs.4551.12$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics
A man borrowed some money and paid back in $3$ equal instalments of Rs. $2160$ each. The rate of interest charged was $20\%$ p.a .compounded annually. Find the total interest charged in Rs.(approximately).
  1. $1928$
  2. $1980$
  3. $1930$
  4. $1954$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  We have, $A=Rs.2,160,\, n=3\, and\, r=20\%$

$\Rightarrow$  First we have to find Sum borrowed i.e. $V$.
$\Rightarrow$  Using, $V=\dfrac{A}{r}[1-(1+r)^{-n}]$


$\Rightarrow$  $V=\dfrac{2160}{0.2}[1-(1.2)^{-3}]$

$\Rightarrow$  $V=10800[1- \dfrac{1000}{(12)^3}]$

$\Rightarrow$  $V=10800[\dfrac{(1728-1000)}{1728}]$

$\Rightarrow$  $V=\dfrac{10800\times 728}{1728}$

$\Rightarrow$  $V=Rs.4550$.
$\Rightarrow$  Total interest = $(A\times n)-V=2160\times 3-4550=Rs. 1930$

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

Mr Dev purchased a car paying Rs $90,000$ and promising to pay Rs 5000 every 3 months for the next 10 years. The interest is $6$% p.a. compounded quarterly. What is the cash value (approximately) of the car ?

  1. 238467

  2. 235467

  3. 228467

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $A=Rs.5000,\, n=40$ and $I=\dfrac{6}{100}\times \dfrac{1}{4}=0.015$

$\Rightarrow$  $V=\dfrac{A}{I}[1-(1+I)^{-n}]$

$\Rightarrow$  $V=\dfrac{5000}{0.015}[1-(1+0.015)^{-40}]$      ---   ( 1 )

$\Rightarrow$  Let $x=(1.015)^{-40}$
$\Rightarrow$  $log\, x=-40(0.0064)$
$\Rightarrow$  $log\, x=-0.256=(\bar{1}.7440)$
$\Rightarrow$   $x=antilog (\bar{1}.7440)$
$\Rightarrow$   $x=0.5546$
     Substitute this value in ( 1 ),
$\Rightarrow$  $V=\dfrac{5000}{0.015}(1-0.5546)$

$\Rightarrow$  $V=\dfrac{5000}{0.015}\times 0.4454=Rs.148466.67$

$\therefore$   Total cash value of the car = $Rs.90000+Rs.148466.67$
$\Rightarrow$  Total cash value of car = $Rs.2,38,467$ approx.