Tag: compound interest formula with different successive rate of interest

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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
A Correct answer