Find the compound interest on 12600 for 2 years 4 months at 10% per annum compounded yearly

Sum

Find CI on Rs. 12600 for 2 years at 10% per annum compounded annually.

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Solution

We have,

A = P`(1 + R/100)^n`, where Principal (P) = ₹ 12600, Rate (R) = 10, Number of years (n) = 2

= ₹ 12600`(1 + 10/100)^2`

= ₹ 12600`(11/10)^2`

= ₹ `12600 xx 11/10 xx 11/10`

= ₹ 15246.

CI = A - P

= ₹ 15246 - ₹ 12600 

= ₹ 2646.

Concept: Deducing a Formula for Compound Interest

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Example 11 - Chapter 8 Class 8 Comparing Quantities

Last updated at Nov. 12, 2018 by

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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

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 $n > 1$.

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