Tag: investement and financial planning

Questions Related to investement and financial planning

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?

investement and financial planning banking compound interest comparing quantity maths

  1. 12 %

  2. 14 %

  3. 16 %

  4. 18 %

Show answer
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?

investement and financial planning banking compound interest comparing quantity maths

  1. $9$

  2. $10$

  3. $11$

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

Show answer
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? 

investement and financial planning banking compound interest comparing quantity maths

  1. $Rs.15000$

  2. $Rs.20000$

  3. $Rs.18000$

  4. $Rs.22000$

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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. 

investement and financial planning banking compound interest comparing quantity maths

  1. $ $1324 $

  2. $ $1456.4 $

  3. $ $1856.4 $

  4. $ $884 $

Show answer
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

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. $27.59$

  2. Rs. $28.10$

  3. Rs. $27.81$

  4. Rs. $28.14$

Show answer
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.

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. $33333.34$

  2. Rs. $33344.64$

  3. Rs. $36543.45$

  4. Rs. $54600$

Show answer
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

investement and financial planning banking compound interest comparing quantity maths

  1. Rs $360$

  2. Rs $350$

  3. Rs $340$

  4. Rs $300$

Show answer
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?

investement and financial planning banking compound interest comparing quantity maths

  1. $50\%$

  2. $60\%$

  3. $70\%$

  4. $80\%$

Show answer
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.

investement and financial planning banking compound interest comparing quantity maths

  1. $Rs. 1,60,800$

  2. $Rs. 1,66,800$

  3. $Rs. 1,68,800$

  4. $Rs. 1,60,000$

Show answer
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?

investement and financial planning banking compound interest comparing quantity maths

  1. Rs 9466.54

  2. Rs 9646.54

  3. Rs 9566.54

  4. Rs 9456.54

Show answer
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 $