Tag: business mathematics and statistics

Quizzes (14) Questions (285)

Questions Related to business mathematics and statistics

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

Rs. $200$ is invested at the end of each month in an account paying interest $6\%$ per year compounded monthly. What is the future value of this annuity after $10$th payment? Given that $(1.005)^{10}=1.0511$.

  1. $2,044$
  2. $2,404$
  3. $2,440$
  4. $2,004$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A$=$Rs. $200$
$n=10$
i$=6\%$ p.a. $=6/12\%$ per month $=0.005$
Future value of annuity after $10$ months is given by
A(n, i)$=A\left[\displaystyle\frac{(1+i)^n-1}{i}\right]$
$A(10, 0.005)=200\left[\displaystyle\frac{(1+0.005)^{10}-1}{0.005}\right]$
$=$Rs. $2,044$.

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

Belose Infrastructures  just issued 10 million Rs100-par bonds payable carrying 8% coupon rate and maturing in 5 years. The bond indenture requires GI to set up a sinking up to pay off the bond at the maturity date. Semi-annual payments are to be made to the fund which is expected to earn 10% per annum. Find the amount of required periodic contributions.

  1. 7905155

  2. 7950515

  3. 8950515

  4. 6950515
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a sinking fund problem. The periodic payment is calculated using the formula for an annuity: PMT = FV * i / ((1+i)^n - 1). With semi-annual periods, n=10 and i=0.05.

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

Find the future value of an annuity of Rs. $500$ made annually for $7$ years at interest rate of $14\%$ compounded annually. Given that $(1.14)^7=2.5023$.

  1. $5,563.25$
  2. $5,365.35$
  3. $5,365.53$
  4. $5,356.35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Annual payment A$=$Rs. $500$
$n=7$
$i=14\%=0.14$
$A(7, 0.14)=500\left[\displaystyle\frac{(1+1.014)^7-1}{0.14}\right]$
$=$Rs. $5365.35$

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

A limited company intends to create a depreciation fund to replace at the end of the 25th year assets costing Rs 100000.Calculate the amount (approximately) to be retained out of profits every year if the interest rate is 3%.

  1. 2755

  2. 3245

  3. 5431

  4. 1200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a sinking fund calculation to reach a future value of 100,000 in 25 years at 3% interest. Using the formula PMT = FV * i / ((1+i)^n - 1), the result is approximately 2755.

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

Veena is allotted an LIG flat for which she has to make an immediate payment of $ $ 100,000$ and $10$ semi-annual payments of $ $50,000$ each, the first being made at the end of $3$ years. If money is worth $10\%$ per annum compounded half-yearly, find the cash price (in $) of the flat.

  1. $302,509$
  2. $400,509$
  3. $302,009$
  4. $402,509$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  Cash price = Down payment + Present value of annuity    --- ( 1 )

$\Rightarrow$  Here, down payment is $\$100,000$, while we have annuity 10 terms i.e. $n$, deferred for $2\dfrac{1}{2}$ years i.e. 5 terms.
$\Rightarrow$  Each installment, $A = \$50,000$
$\Rightarrow$  Rate of interest, $r=10\%\, p.a.$ compounded half-yearly = 0.05
$\Rightarrow$  $m=5$ and $m+n=15$
$\therefore$  Present value of annuity,
$\Rightarrow$  $V=\dfrac{A}{r}\times [\dfrac{1}{(1+r)^m}-\dfrac{1}{(1+r)^{m+n}}]$
$\Rightarrow$  $\dfrac{50,000}{0.05}\times [(1.05)^{-5}-(1.05)^{-15}]$
$\Rightarrow$  $\$ 302509.07$
Now, from ( 1 )
$\Rightarrow$  Cash price of the flat = $\$100,000+\$302,509=\$402,509$

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

An investor deposits Rs 1000 in a saving institution. Each payment is made at the end of year.If the payment deposited earns 12% interest compounded annually how much amount(approximately) will he receive at the end of 10 years.

  1. $1234$
  2. $2345$
  3. $17548$
  4. $4567$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$P=Rs.1000,r=12\%,t=10$

$A=\sum _{ n=1 }^{ 9 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n }+P } \ =\sum _{ n=1 }^{ 9 }{ 1000{ (1+\cfrac { 12 }{ 100 } ) }^{ n }+1000 } \ =3000\times 16.548\ =Rs.17548$

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

A machine costing Rs $2$ lacs has effective life of $7$ years and its scrap value is Rs $30000$. What amount (in Rs) should the company put into a sinking fund earning $5\%$ per annum so that it can replace the machine after its useful life? Assume that a new machine will cost Rs $3$ lacs after $7$ years.

  1. $30161.35$
  2. $33101.35$
  3. $33161.35$
  4. $33111.35$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Cost of new machine is $Rs.3\,lacs$

$\Rightarrow$  Scrap value of old machine is $Rs.30000$
$\Rightarrow$  Hence, money required for new machine after 7 years  = $Rs.300000-Rs.30000=Rs.270000$.
$\Rightarrow$  If A is the annual deposit into sinking fund, then we have
$\Rightarrow$  Amount of annuity, $M=Rs.270000$
$\Rightarrow$  Number of periods = $7\, years$
$\Rightarrow$  $r=5\%=0.05$
$\therefore$   $M=\dfrac{A}{r}\times [(1+r)^n - 1]$
$\Rightarrow$  $270000=\dfrac{A}{0.05}\times[(1.05)^7-1]$

$\Rightarrow$  $A=\dfrac{270000\times 0.05}{(1.05)^7 - 1}$

$\therefore$   $A=33161.35$ Rs

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

A man decides to deposit Rs 3000 at the end of each year in a bank which pays 3% p.a compound interest . If the instalments are allowed to accumulate , what will be the total accumulation at the end of 15 years.

  1. Rs.$57450$
  2. Rs.$67780$
  3. Rs.$67050$
  4. Rs.$98450$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.3000,r=3\%,t=15$
$A=\sum _{ n=1 }^{ 15 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ 15 }{ 3000{ (1+\cfrac { 3 }{ 100 } ) }^{ n } } \ =3000\times 19.15\ =Rs.57450$

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

Find the present value of a sequence of annual payments of Rs 25000 each , the first being made at the  end of 5th year and the last being paid at the end of 12th year, if money is worth 6%.

  1. $122875$
  2. $102875$
  3. $132875$

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

We know that formula of present value is 

$V=\cfrac{A}{r}[\cfrac{1}{(1+\cfrac{R}{100})^m}$$-\cfrac{1}{(1+\cfrac{R}{100})^{m+n}}]$
We have  annuity of $8$ terms $(n)$
For $4$ terms $(m)\implies m=4\ \implies m+n=12$
$V=\cfrac{25000}{0.06}[\cfrac{1}{(1+\cfrac{6}{100})^4}$$-\cfrac{1}{(1+\cfrac{6}{100})^{12}}]=Rs.122968.45$