Tag: compound interest ( for different time period)

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Questions Related to compound interest ( for different time period)

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

The compound interest on Rs. 50,000 at 4% per annum for two years compounded anually is :

  1. $4000$
  2. $4080$
  3. $4280$
  4. $4050$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

C.I. = Amount - Principle

=> $P((1+\dfrac{r}{100})^{T} _{} - 1)$
CI = $50,000(1+\dfrac{4}{100})^{2} _{} - 1)$
C.I.= $4080.$

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

At what rate percent per annum will a sum of Rs. $2000$ amount to Rs. $2205$ in $2$ years at compound interest?

  1. $3$%
  2. $2$%
  3. $5$%
  4. $4$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  $P=$Rs.$2000,\,A=$Rs.$2205$ and $T=2\,$years.

$\Rightarrow$  $A=P(1+\dfrac{R}{100})^T$

$\Rightarrow$  $2205=2000\times (1+\dfrac{R}{100})^2$

$\Rightarrow$  $\dfrac{441}{400}=(1+\dfrac{R}{100})^2$

$\Rightarrow$  $\dfrac{21}{20}=(1+\dfrac{R}{100})$

$\Rightarrow$  $R=\dfrac{1}{20}\times 100=5\%$

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

The cost of a car purchased 2 years ago depreciates at the rate of 20% per annum. If its present value is Rs 3, 15,600, find the value of the car after 2 years

  1. Rs 2,01,994

  2. Rs 50,496

  3. Rs 2,01,984

  4. Rs 10,09,920
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Depreciation = A=P\left (1-\frac {r}{100}\right )^n=3,15,600\left (1-\frac {20}{100}\right )^2$
$=3,15,600\left (\frac {4}{5}\right )^2=3,15,600\times \frac {16}{25}=Rs 2,01,984$

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

What sum will amount to Rs. $32,967$ in $2$ years C.I., if the rates are $10$ per cent and $11$ per cent for the successive years?

  1. Rs. $25,000$
  2. Rs. $26,000$
  3. Rs. $27,000$
  4. Rs. $28,000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  $P=$Rs.$32,967,\,R _1=10\%,\,R _2=11\%$


$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})\times (1+\dfrac{R _2}{100})$

$\Rightarrow$  $32967=P\times (1+\dfrac{10}{100})\times (1+\dfrac{11}{100})$

$\Rightarrow$  $32967=P\times \dfrac{11}{10}\times \dfrac{111}{100}$

$\Rightarrow$  $P=\dfrac{32967\times 1000}{1221}=27\times 1000=$Rs. $27,000$

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

What sum will amount to Rs. $65,934$ in $2$ years C.I., if the rates are $10$ per cent and $11$ per cent for the successive years?

  1. $53,000$
  2. $54,000$
  3. $55,000$
  4. $60,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A _1=P(1+\cfrac{10}{100})^1=P\times 1.1$
$A _2=A _1(1+\cfrac{11}{100})^1=P\times 1.221$
$\implies 65934=1.221P\\ \implies p=54,000$
Hence sum$=Rs.54,000$

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

Read the following statement carefully and select the correct option 
statement - i : An article marked at rs 800 is sold at successive discount of 15% and 25%. If the buyer desires to sell. it off at a profit of 20% after allowing a 10% discount, then his marked price will be rs 680.
Statement- ii; if the amount of Rs p at 10% per annum for 3 year compounded annually becomes rs q, then q ; p is 125 ; 216.

  1. Both statement- i and statement- ii are false

  2. Both statement- i and statement- ii are true

  3. Both statement- 1 is true but statement- 11 are false

  4. statement - 1 is false but statement -11 is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

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.

  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

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

$\Rightarrow 5667.20  Rs.$

$C.I.=5667.20-4600=1067.20  Rs.$

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

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?

  1. $Rs.\ 2583$
  2. $Rs.\ 2460$
  3. $Rs.\ 2370$
  4. $Rs.\ 2860$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The deposit is made on the first day of each year for two years, meaning two installments of 1200 are made at t = 0 and t = 1 year. Compounding this at 5 percent for the appropriate periods up to the tenth day of the second year yields 2460.

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

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

  1. $15$ years
  2. $12$ years
  3. $36$ years
  4. $21$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At compound interest, if a sum becomes 3 times in 4 years, it will become 3^3 = 27 times in 4 * 3 = 12 years. Each 4-year period multiplies the principal by 3.