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Multiple choice investement and financial planning banking compound interest comparing quantity maths

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. $Rs.400$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Ajay's investment be x and his time be 12 months. Anil's investment is x + 300 and his time is 6 months. Ratio of their profits: Ajay's share = Rs. (200 + 25) = Rs. 200, Anil's share = Rs. (200 - 25) = Rs. 175 since total profit is 375 and Ajay got 25 more than Anil. Ratio of profits = Ajay / Anil = 200 / 175 = 8 / 7. Also, ratio of profits equals ratio of (investment * time): (x * 12) / ((x + 300) * 6) = 2x / (x + 300). Equating these gives 2x / (x + 300) = 8 / 7, meaning 14x = 8x + 2400, so 6x = 2400, x = 400. Anil's investment is x + 300 = 700.

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $x=12000 Rs$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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 %
Reveal answer Fill a bubble to check yourself
C Correct answer
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=$\frac{52}{325}\times 100=16$


Multiple choice investement and financial planning banking compound interest comparing quantity maths

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. $11\displaystyle \frac{1}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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
$\Rightarrow 35+15x=170$
$\Rightarrow 15x=170-35$
$\Rightarrow 15x=135$
$\Rightarrow x=\frac{135}{15}=9$
                     

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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 $
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=$ $400+440+484+532.40=1856.40$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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. $28.14$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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. $54600$
Reveal answer Fill a bubble to check yourself
A Correct answer
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. $33333.34$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

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 $300$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $Rs.360$