Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

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 $(1.005)^{10}=1.0511$.

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

  1. $2,044$

  2. $2,404$

  3. $2,440$

  4. $2,004$

Show answer
Correct Option: A
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. $2,044$.

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.

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

  1. 7905155

  2. 7950515

  3. 8950515

  4. 6950515

Show answer
Correct Option: B

An annuity is?

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

  1. A fixed sum

  2. Paid at regular intervals

  3. Under certain stated conditions

  4. All of the above

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Correct Option: D
Explanation:

An annuity is 

$(1)$A fixed sum
$(2)$ Paid at regular intervals
$(3)$Under certain stated conditions.

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

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

  1. $5,563.25$

  2. $5,365.35$

  3. $5,365.53$

  4. $5,356.35$

Show answer
Correct Option: B
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. $5365.35$

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%.

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

  1. 2755

  2. 3245

  3. 5431

  4. 1200

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Correct Option: A

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.

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

  1. $302,509$

  2. $400,509$

  3. $302,009$

  4. $402,509$

Show answer
Correct Option: D
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 = $\$100,000+\$302,509=\$402,509$

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.

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

  1. $1234$

  2. $2345$

  3. $17548$

  4. $4567$

Show answer
Correct Option: C
Explanation:

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

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

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.

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

  1. $30161.35$

  2. $33101.35$

  3. $33161.35$

  4. $33111.35$

Show answer
Correct Option: C
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

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.

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

  1. Rs.$57450$

  2. Rs.$67780$

  3. Rs.$67050$

  4. Rs.$98450$

Show answer
Correct Option: A
Explanation:

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

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%.

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

  1. $122875$

  2. $102875$

  3. $132875$

  4. None of the above

Show answer
Correct Option: D
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$