What is the compound interest in ₹ on a sum of ₹ 12600 for 11 2 years at 20% per annum if the interest is compounded half yearly?

Find the CI on Rs 12,600 for 2 years at 10% per annum compounded annually.

Answer

Verified

Hint:This is a problem related to Compound Interest (CI). To find out the CI, principal amount, rate of interest and number of years for which the interest to be calculated have been given in the problem. Put these values in the standard formula to calculate CI. The standard formula to calculate final amount is as $A = P{(1 + \dfrac{R}{{100}})^n}$

Complete step-by-step answer:
Now, to calculate the compound interest, we should know the final amount after the given years, which can be expressed as
$A = P{(1 + \dfrac{R}{{100}})^n}{\text{ }}...................{\text{ (1)}}$
Where $A$ is the final amount, $P$ is the principal amount, $R$ is the rate of interest and $n$ is the number of years.
In the question, it is given that
$
  P = 12,600 \\
  R = 10\% {\text{ and}} \\
  n = 2{\text{ years}} $
Now, putting these values in the equation (1) above, we will get the following expression,
$
  A = 12600 \times {(1 + \dfrac{{10}}{{100}})^2} \\
  A = 12600 \times {(\dfrac{{11}}{{10}})^2} \\
  A = 12600 \times \dfrac{{121}}{{100}} \\
  A = 126 \times 121 \\
  A = 15246 $
Now, we already know that $P$ is the principal amount 12,600
Hence, interest compounded $CI$ in 2 years is as below,
$
  CI = A - P \\
  CI = 15246 - 12600 \\
  CI = 2646 $
Thus, the answer to the question, the Interest Compound $CI$ is Rs 2,646.

Note:Interest to the principal amount is of two types.
1.Simple Interest
2.Compound Interest
Both these interests are different in nature. The final amount with simple interest can be calculated in the following way,
$A = P(1 + \dfrac{R}{{100}} \times n){\text{ }}.............{\text{ (2)}}$,
Where $A$ is the final amount, $P$ is the principal amount, $R$ is the rate of interest and $n$is the number of years.
You can easily understand from the two formulae, eq. (1) and (2), that the final amount calculated from these two formulae are very different and the amount calculated with formula (1) is higher as compared to the amount calculated with formula (2) when $n > 1$.

Example 11 - Chapter 8 Class 8 Comparing Quantities

Last updated at Nov. 12, 2018 by

Solve all your doubts with Teachoo Black (new monthly pack available now!)

Transcript

Example 11 Find CI on Rs 12600 for 2 years at 10% per annum compounded annually.Given, Principal (P) = 12600 Time = 2 Years Rate (R) = 10% per annum We use the formula A = P ("1 + " 𝑟/100)^𝑛 where A = Amount after n years A = 12600 ("1 + " 10/100)^2 = 12600 ("1 + " 1/10)^2 = 12600 ((10 + 1)/10)^2 = 12600 (11/10)^2 = 12600 (11/10)^2 = 12600 × 121/100 = 126 × 121 = 15246 ∴ Amount after 2 years = Rs 15,246 Now, Amount = Principal + Interest 15246 = 12600 + Interest 15246 – 12600 = Interest 2646 = Interest Interest = 2646 ∴ Compound Interest = Rs 2,646

compound interest on rupees 12000 for 2 years at 10% 20% per annum compounded half-yearly ok give information is that time is given by two years ok and rate 20% per annum India principle which is given rupees 12000 first of all we will calculate the amount after that we will calculate the compound interest for calculating the amount that amount is equal to Prince oneplus RX100 whole to the power and the time the rate of interest is the principal and so here is the time so time is two years

but question is asking compounded half-yearly so in one year there are two half yearly and each of six months so in a two year total half yearly we will multiply with two equal to four half yearly and the rate at which is given as 20% per annum ok latest 20% per annum but we need to have fun so 20% per annum for half yearly so we will / / to so this is equal to 10% half yearly ok now will substitute the values so this is equal to the amount can be calculated by 12000 into one plus rate 10 app on Android V to the power 2

4 ok now further simplify so amount will be equal to 12000 and your 10 cancelled and 1 + 1 upon time will take LCM LCM of 10 and 10 plus 111 11.10 whole to the power 4 get a simplified 12000 into this can be written as 11 upon 10 into 11 of content into 11.10 1110 ok now we will simply 50 10 20 30 days will be cancelled out with this 30 and here 12 into 11 to 11 letters 121 and eleven to eleven it is also 121 ok

this is divided by 10 ok this is equal to 17 5692 and divided by 10 finally we get 1756 9.2 and in Rupees and also we know that compound interest will be equal to amount - pencil so I want we are already calculated sir compound interest will be equal to 1756 9.2 - 12000 and this is equal to 55 69.2 ok compound interest that is TI final that the required compound interest

which is given as rupees 55 6922 final answer this question thank you