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Investement and financial planning - class-IX

Description: investement and financial planning
Number of Questions: 21
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Investment in funds like ELSS are admissible for deduction under section $80\text{C}$ of income tax.

  1. True

  2. False


Correct Option: A
Explanation:

Investments in Equity Linked Saving Schemes or ELSS qualify for tax deduction under Section $80C$ of the Income Tax Act. The maximum tax deduction allowed under Section $80C$ is Rs 1.5 lakh under Section $80C$.

You invest Rs. $3,000$ in a two year investment that pays you $12\%$ p.a. Calculate the future value of the investment.

  1. Rs. $3,367.20$

  2. Rs. $3,673.20$

  3. Rs. $3,763.20$

  4. Rs. $3,736.20$


Correct Option: C
Explanation:

$F=C.F. (1+i)^n$
Where, $F=$ Future value
$C.F. =$ Cash flow $=$Rs. $3,000$
$i=$ rate of interest $=0.12$
$n=$ time period $=2$
$F=$Rs. $3,000(1+0.12)^2$
$=$Rs. $3,000\times 1.2544$
$=$Rs. $3,763.20$

Which statement is wrong regarding Systematic Investment Plan:

  1. Advantage of long terms and short-term gains

  2. It has huge risks but high returns

  3. Redemption of units can be done

  4. Safe and transparent mode of investment


Correct Option: B
Explanation:

Systematic Investment Plan (SIP) is an investment vehicle offered by mutual funds to investors, allowing them to invest small amounts periodically instead of lump sums. It is good for investors who don't have much financial market's understanding. It involves lesser risks and low returns because investment is done in small amounts over a period of time.

A man borrows $Rs. 6000$ at $5\% $ $C.I.$ per annum$.$ if the repays $Rs.1200$ at the end of the each year$,$ find the amount of the loan outstanding at the beginning of the third year$.$ 

  1. Rs 4155.0

  2. Rs 5555.5

  3. Rs 5452.0

  4. Rs 4452.5

  5. None of these


Correct Option: A
Explanation:
Given Principle amount $= Rs . 6000$
And$,$
Rate of interest $= r = 5\% $ compounded annually

So$,$
Interest after $1 year = 6000 × \dfrac{5}{100} × 1 = 60× 5 = Rs . 300$
Total money owed after $1 year = 6000 + 300 = 6300$

And$,$
$Rs. 1200$ paid $,$ So
Total money starting of second year $= 6300 - 1200 = Rs.5100$

And$,$
Interest after $2 year = 5100 × 5 × 1100 = 51× 5 = Rs . 255$
money owned after $2 year = 5100 + 255 = 5355$

And$,$
$Rs. 1200$ paid $,$ So
Total money outstanding starting of Third year $= 5355 - 1200$ $= Rs.4155$

Hence,
option $(A)$ is correct answer.

A man borrowed Rs.4000 at 10% per annum compound interest.At the end of each year he has repaid Rs.1000.The amount of money he still incurs after the third year is -------- .

  1. Rs.2740

  2. Rs.2104

  3. Rs.2014

  4. Rs.3400


Correct Option: C

Mutual Fund is a professionally managed investment scheme, run by an AMC i.e. Asset Management Company and they invest their own money in different schemes.

  1. True

  2. False


Correct Option: B
Explanation:

Mutual Fund is a professionally managed investment scheme, which is run by AMC. Mutual Fund is a mediator that brings together a group of people and invests 'their' money in stocks, bonds and other securities.

The price of a T.V. set worth Rs. 20,000 is to be paid in 20 instalments of Rs. 1000, each. If the rate of interest be 6% per annum, and th6 first instalment be paid at the time of purchase, then, the value of the last instalment covering the interest as well will be : (Hotel Management, 1998)

  1. Rs. 1050

  2. Rs. 2050

  3. Rs. 3000

  4. None of these


Correct Option: A

The profit of a company (whose capital is divided into 25, 000 shares of Rs. 10 each) for the last three years are: Rs. 50, 000; Rs. 60, 000 and Rs. 40, 000. The fair return on investment is taken at 10% p.a. The value of company's share will be __________.

  1. Rs. 10

  2. Rs. 20

  3. Rs. 30

  4. Rs. 40


Correct Option: B

Ajay and Anil start a business in partnership. Anil invested $Rs.300$ more that Ajay for half the number of months that Ajay did. If, out of the total profit of $Rs.375$ of the one year, Ajay got $Rs.25$ more than Anil, what was the investment made by Anil?  

  1. $Rs.800$

  2. $Rs.350$

  3. $Rs.700$

  4. $Rs.400$


Correct Option: B

Mr. Dua invested money in two schemes P and Q offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a respectively. if the total amount of interest accrued two schemes together in two years was Rs 4818.30 and the total amount invested was Rs 27, 000, what was the amount invested in Scheme P?

  1. Rs 12, 000

  2. Rs 13,500

  3. Rs 15, 000

  4. None of these


Correct Option: A
Explanation:

Let p invested Rs x Then q invested Rs $(27000-x)$
$\therefore x(1+\dfrac{8}{100})^{2}-1+(27000-x)(1+\dfrac{9}{100})^{2}-1=4818.30$
$\Rightarrow (x\times \dfrac{104}{625})+\dfrac{1881(27000-x)}{10000}= \dfrac{481830}{100}$
$\Rightarrow 1664x+1881(27000-x)=48183000$
$\Rightarrow (1881x-1664x)=50787000-48183000$
 Or $217x=2604000$
  Or $x=12000 Rs$

A family made a down payment of $75 and borrowed a set of encyclopedias that cost $400. The balance with interest was paid in 23 monthly payments of $16 each and a final payment of $9. What was the per cent of interest to the borrowed sum?

  1. 12 %

  2. 14 %

  3. 16 %

  4. 18 %


Correct Option: C
Explanation:

Total cost =$ 400
Down payment=$ 75
Remaining amount=$400-75=$ 325$
Balanced paid in 24 months=$23 \times 16+9=$ 377$
Difference=$377-325=$52$
The per cent of interest to the borrowed sum=$\frac{52}{325}\times 100=16$


A $500 investment and a $1,500 investment have a combined yearly return of 8.5 per cent of the total of the two investments. If $500 investment has a yearly return of 7 per cent, what per cent yearly return does the $1,500 investment have?

  1. $9$

  2. $10$

  3. $11$

  4. $11\displaystyle \frac{1}{9}$


Correct Option: A
Explanation:

Total investment by A=$500+1500=2000$
Yearly return =8.5 % of 2000
$\Rightarrow \frac{8.5}{100}\times2000=170$
Yearly return of 500=7% of 500
$\Rightarrow \frac{7}{100}\times500=35$
Let yearly return of 1500 is x
Yearly return=x% of 1500
$\Rightarrow \frac{x}{100}\times 1500=15x$
Then according to the question
$\Rightarrow 35+15x=170$
$\Rightarrow 15x=170-35$
$\Rightarrow 15x=135$
$\Rightarrow x=\frac{135}{15}=9$
                     

$A$ started a business with a capital of $Rs.10000$. Four month later, $B$ joined him and $2$ more moth letter , $C$ joined them in the partnership. If at the end of the year, all of them got an equal shares of profit, what was $C's$ investment? 

  1. $Rs.15000$

  2. $Rs.20000$

  3. $Rs.18000$

  4. $Rs.22000$


Correct Option: A

A person pays $ $400$ every year as loan installments to a bank. If every year bank increases the installment amount by $10$%, the find the total amount he pays in installments in $4$ years. 

  1. $ $1324 $

  2. $ $1456.4 $

  3. $ $1856.4 $

  4. $ $884 $


Correct Option: C
Explanation:

Given  person pays $400$ every as loan installments to bank

And every year bank increases installments $10\%$ every year 
Then after one year installments $=$ $400\times \dfrac{110}{100}=$440$
And after two year installments$440\times \dfrac{110}{100}=$484$
And after three year installments$484\times \dfrac{110}{100}=$532.40$
Then person paid installments in $4$ years $=$ $400+440+484+532.40=1856.40$

A man borrows Rs. $200$ at $ 5$% compound interest. At the end of each year he pays back Rs. $50$. At the end of $4 $ years he owes

  1. Rs. $27.59$

  2. Rs. $28.10$

  3. Rs. $27.81$

  4. Rs. $28.14$


Correct Option: A
Explanation:

Amount of one year

$\displaystyle=200\left[1+\frac{5}{100}\right]$

$\displaystyle=200\times\frac{21}{20}=210$

$\therefore$ At the end of year he pays back Rs. 50. So the principal for the second year is Rs. 160.
$\therefore$ Amount of Second year

$\displaystyle=160\left[1+\frac{5}{100}\right]$

$\displaystyle=160\times\frac{21}{20}=168$

$\therefore$ At the end of year he pays back Rs. 50. 
So rest amount = 168 -50 = Rs. 118.
This amount is principal amount for third year.
$\therefore$ Amount of third year

$\displaystyle=118\left[1+\frac{5}{100}\right]$

$\displaystyle=118\times\frac{21}{20}=123.90$

At the end of years he pays back Rs. 50.
So rest amount
$=123.90-50=Rs. 73.90$
This amount is principal for fourth year.
$\therefore$ Amount of fourth year

$\displaystyle=73.90\left[1+\frac{5}{100}\right]$

$\displaystyle=73.90\times\frac{21}{20}=77.59$

At the end of year he pays back Rs. 50.
So rest amount
$=77.595-50=Rs. 27.59$
$\therefore$ At the end of fourth year he owes Rs. 27.59.

Lakshman borrowed Rs. $20$ lakhs as housing loan from ICICI at $10\%$ p.a to be repaid in $10$ years. if the EMI is Rs. $2500$ per lakh, find how much he pays as interest in the first month. Find also he principal repaid then.

  1. Rs. $33333.34$

  2. Rs. $33344.64$

  3. Rs. $36543.45$

  4. Rs. $54600$


Correct Option: A
Explanation:

Interest at $10\%$ for the first month for Rs. $20$ lakhs $=$ $2000000 \times \dfrac{1}{12}\times \dfrac{10}{100}=16666.66$
EMI for one month, for $20$ lakhs $= 2500 \times  20 =$ Rs. $50000$
Hence principal repaid $=$ Rs. $50000 - 16666.66 =$ Rs. $33333.34$

A sum of Rs $550$ was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be $20\%$ compounded annually, then the amount of each instalment will be

  1. Rs $360$

  2. Rs $350$

  3. Rs $340$

  4. Rs $300$


Correct Option: B
Explanation:
Let $x$ be each installment
After paying the first installement $x$
the remaininng principle is $ 550\times1.2-x$
This then compounded yearly should be equal to the second installment
$\left(550\times1.2-x\right)\times 1.2= x$
$ 550\times 1.2^2-x\times 1.2 = x$
$792=2.2\times x$
$x=360$
Thus eachn installemnt should be $Rs.360$

A television set is sold for Rs. $10000$ cash on Rs. $2000$ cash down followed by six equal instalments of Rs. $1600$ each. What is the rate of interest?

  1. $50\%$

  2. $60\%$

  3. $70\%$

  4. $80\%$


Correct Option: B
Explanation:

Given, $n = 6, I =$ Rs. $1600$, 

$E = 2000 + 6 \times  1600 - 10000 = $ Rs. $1600$
We know $R = \dfrac{2400E}{n(n+1)I-2E}$
$\Rightarrow R = \dfrac{2400\times 1600}{6(6+1)1600-2\times 1600}$
$\Rightarrow R = 60\%$
Thus, the rate of interest is $60\%$.

Raghav buys a shop for $Rs. 1,20,000$. He pays half of the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs. 5000$ each. If the rate of interest is $12\%$ and he pays with the installment the interest due on the unpaid amount find the total cost of the shop.

  1. $Rs. 1,60,800$

  2. $Rs. 1,66,800$

  3. $Rs. 1,68,800$

  4. $Rs. 1,60,000$


Correct Option: B
Explanation:
Given that: 
Raghav buys a shop for $Rs.1,20,000.$
He pays half of the amount in cash $= \dfrac{120000}{2}\Rightarrow Rs.60,000$

Balance amount to be paid $= 120000 - 60000 \Rightarrow Rs. 60000.$

Given that amount of each installment $=Rs. 5000.$

He agrees to pay the balance in $12$ annual installments with interest of $12\%.$

 Amount of the $1^{st}$ installment 
$\Rightarrow 5000 + \dfrac{12}{100}\times   60000$

$\Rightarrow 5000 + 600 \times 12$

$\Rightarrow 5000 + 7200$

$\Rightarrow Rs. 12,200.$


 Amount of the $2^{nd}$ installment
$ \Rightarrow 5000 + \dfrac{12}{100} \times (60000 - 5000)$
$\Rightarrow 5000 + \dfrac{12}{100}\times  55000$
$\Rightarrow 5000 + 550 \times 12$
$\Rightarrow 5000 + 6600$
$\Rightarrow Rs. 11,600.$

As the amount paid for installment is $12200,11600,....... $ so It forms an $AP.$

The first term $a = 12,200$
Common Difference $d =  11600 - 12200\Rightarrow-600$
Total number of terms $n = 12.$

We know that sum of $n$ terms in $AP$
$\Rightarrow \dfrac{n}{2}[2a + (n-1) d]$

 Therefore the total cost of the shop
 $\Rightarrow 60000 +\dfrac{ 12}{2}[2(12200) + (12-1) \times (-600)]$

$\Rightarrow 60000 + 6(24400 - 6600)$
$\Rightarrow 60000 + 6 \times 17800$
$\Rightarrow 60000 + 106800$
$=Rs. 1,66,800.$

Hence, the total cost of the shop $= Rs.1,66,800.$

What sun will become Rs 9826 in 18 months if the rate of interest is $\displaystyle 1\frac{1}{2}$% per annum and the interest is compounded half-yearly?

  1. Rs 9466.54

  2. Rs 9646.54

  3. Rs 9566.54

  4. Rs 9456.54


Correct Option: A
Explanation:

r $ = 2\dfrac {1}{2} $ % $ = \dfrac {5}{2} $ % n $ = 18 $ months $ = \dfrac {3}{2} $ years

When the interest is compounded half yearly,

$ A=P\left( 1+\dfrac { r }{ 2\times 100 }  \right) ^{ n\times 2 } $

$ => 9826 = P\left( 1+\dfrac { \dfrac {5}{2} }{ 2\times 100 }  \right) ^{ \dfrac {3}{2}\times 2 } $
$ => 9826 = P( \dfrac {81}{80}) ^{ 3 } $
$ => P =Rs 9466.54 $

The NAV of a unit in mutual fund scheme is Rs $10.65$, then find the amount required to buy $500$ such units.

  1. Rs.$5325$

  2. Rs.$5235$

  3. Rs.$53250$

  4. Rs.$5350$


Correct Option: A
Explanation:

Amount required to buy $500$ such units

$=10.62\times500$
 $=Rs.5325$

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