Tag: mathematics and statistics

Questions Related to mathematics and statistics

Calculate the amount and the compound interest on :

Rs. $4,600$ in $2$ years when the rates of interest of successive years are $10$% and $12$% respectively.

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. 5,667.20 and Rs. 1,067.20 

  2. Rs. 5,600.20 and Rs. 167.20 

  3. Rs. 5,680.20 and Rs. 167.20 

  4. Rs. 5,667.20 and Rs. 1,000.20 

Show answer
Correct Option: A
Explanation:

C.I of 4600 for 2 year at rate of interest are 10% and 12%
$Amount=4600\times \left(1+\dfrac{10}{100}  \right)\left(1+\dfrac{12}{100}  \right)$

$\Rightarrow 4600\times \dfrac{110}{100}\times \dfrac{112}{100}$

$\Rightarrow 5667.20  Rs.$

$C.I.=5667.20-4600=1067.20  Rs.$

A man deposits $Rs.\ 1200$ in a bank on the $1st$ day of each year. If the bank pays $5\%$ per annum compound interest on deposited sum of money, what will be the amount to his credit on the $10th$ day of the second year?

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. $Rs.\ 2583$

  2. $Rs.\ 2460$

  3. $Rs.\ 2370$

  4. $Rs.\ 2860$

Show answer
Correct Option: A

The sum on which the compound interest for second year at $10 \% \,p.a.$ is $Rs. \,132$ is given by

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. $Rs. \,100$

  2. $Rs. \,1200$

  3. $Rs. \,1320$

  4. None of these

Show answer
Correct Option: A

A certain sum becomes $3$ times itself in $4$ years at compound interest. In how many years does it become $27$ times itself?

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. $15$ years

  2. $12$ years

  3. $36$ years

  4. $21$ years

Show answer
Correct Option: A

The compound interest on Rs. $2000$ in $2$ years, if the rate of interest is $4 \%$ per annum for the first year and $3\%$ per annum for the second year will be 

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. $142.40$

  2. Rs. $140.40$

  3. Rs. $141.40$

  4. Rs. $143.40$

Show answer
Correct Option: A
Explanation:

Given, $P=$ Rs. $2000$, $\displaystyle r _{1}$ $=4\%$ p.a. for $1^{st}$ year, $\displaystyle r _{2}$ $=3\%$ p.a. for $2^{nd}$ year
$\displaystyle \therefore A=P\left ( 1+\frac{r _{1}}{100} \right )\left ( 1+\frac{r _{2}}{100} \right )$

$=2000\left ( 1+\dfrac{4}{100} \right )\left ( 1+\dfrac{3}{100} \right )$
$\displaystyle =$ Rs. $\left ( 2000\times \dfrac{26}{25}\times \dfrac{103}{100} \right )=$ Rs. $2142.40$
$\displaystyle \therefore$ C.I. $=$ Rs. $2142.40 - $ Rs. $2000=$ Rs. $142.40$

How much will Rs. $9,000$ amount to in $3$ years, at compound interest, if the rates for successive years are $12 \%$, $15 \%$ and $20 \%$ per year respectively?

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. $13810.40$

  2. Rs. $13710.40$

  3. Rs. $13910.40$

  4. Rs. $12910.40$

Show answer
Correct Option: C
Explanation:

$A=9000\times \left(1+\dfrac{12}{100}\right)\left(1+\dfrac{15}{100}\right)\left(1+\dfrac{20}{100}\right)$

$A=9000\times \dfrac{112}{100}\times \dfrac{115}{100}\times \dfrac{120}{100}$

$A=\dfrac{112\times 115\times 12\times 9}{100}$

$A=13910.40  Rs$

Find the amount on Rs. $ 12,500$ for $2$ years compounded annually, the rate of interest being $15\%$ for the first year and $16\%$ for the second year.

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. $16,500$

  2. Rs. $16,750$

  3. Rs. $16,675$

  4. None of these

Show answer
Correct Option: C
Explanation:

Given, $P=$ Rs. $ 12500$,$R _1$ $=15\%$,$R _2 $ $=16\%$
$A = p \left(1 + \displaystyle \frac{R _1}{100} \right) \left(1 + \displaystyle \frac{R _2}{100} \right)$
$A = 12500 \times \left(1 + \displaystyle \frac{15}{100} \right) \times \left(1 \times \displaystyle \frac{16}{100} \right)$
$= 12500 \times \displaystyle \frac{115}{200} \times \frac{116}{100}$
$= $ Rs. $16,675$

A sum of money double itself in 4 years at compound interest.! n how many years it will become eight times at same rate of interest

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. 12 years

  2. 18 years

  3. 24 years

  4. 16 years

Show answer
Correct Option: A
Explanation:

$\displaystyle A = P \left( 1 + \frac {R}{100} \right)^T$

$\displaystyle 2x = x \left( 1 + \frac {R}{100} \right)^4$

$\displaystyle \left( 1 + \frac {R}{100} \right) = 2^{1/4}$

$\displaystyle 8x=x \left( 1 + \frac {R} {100}\right)^T$

$\displaystyle \because 1 + \frac {R} {100} = 2^{1/4}$

$\displaystyle  \therefore 8=2^{T/4}$

$\displaystyle 2^3 = 2^{T/4}$

$\displaystyle \frac {T}{4}=3$

$T=12\, years$

Sam invested Rs. $15000$ at the rate of $10 \%$ per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be:

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. Rs. $16,500$

  2. Rs. $16,525.50$

  3. Rs. $16,537.50$

  4. Rs. $18,150$

Show answer
Correct Option: C
Explanation:

$P =$ Rs. $15000$; $R =10 \%$ p.a $= 5 \%$ per half-year; $T= 1$ year $= 2$ half-years.
$\therefore$ Amount $=\, \left [ 15000\, \times\, \left ( 1\,+\, \displaystyle \frac{5}{100} \right )^2 \right ]$
$=$ Rs. $\left ( 15000\, \times\, \displaystyle \frac{21}{20}\, \times\, \frac{21}{20} \right )$
$= 16,537.50$

There is a question followed by three statements. While answering the question, you may or may not require the data provided in all the statements. You have to read, the question and the three statements and then decide whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question. Mr. Gupta borrowed a sum of money on compound interest. What will be the amount to be repaid if he is repaying the entire amount at the end of $2$ years?

$I$. The rate of interest is $5$ p.c.p.a.
$II$. Simple interest fetched on the same amount in one year is $Rs. 600$.
$III$. The amount borrowed is $10$ times the simple interest in $2$ years.

mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

  1. $I$ only

  2. $III$ only

  3. $I$ or $II$ only

  4. None of these

Show answer
Correct Option: D
Explanation:

Given 
I. The rate of interest is 5 p.c.p.a.
II. Simple interest fetched on the same amount in one year is Rs. 600.
III. The amount borrowed is 10 times the simple interest in 2 years.
Now | and || give the sum,
For this sum , C.I and hence amount can be obtained
Thus , ||| is redundant
Again || gives S.I for 2 years =$600\times 2=1200$
Now from ||| ,sum =$10\times 1200=12000$
Thus Rate=$\frac{100\times 1200}{2\times 1200}=5%$p.a
Thus ,C.I for 2 years and therefore ,amount can be obtained.
Thus ,| is redundent
Hence either  |  and II  or II and III are sufficient to answer the question