Answer  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 12,600Hence, 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 Interest2.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 $n > 1$.
Last updated at Nov. 12, 2018 by Teachoo
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Last updated at Nov. 12, 2018 by Teachoo
Support Teachoo in making more (and better content) - Monthly, 6 monthly, yearly packs available!
Saving
The power of compounding grows your savings faster 3 minutes
The sooner you start to save, the more you'll earn with compound interest. Compound interest is the interest you get on:
For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest. This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest. Save more with compound interestThe power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later. For example, if you put $10,000 into a savings account with 3% interest compounded monthly:
Compound interest formulaTo calculate compound interest, use the formula: A = P x (1 + r)n A = ending balanceP = starting balance (or principal)r = interest rate per period as a decimal (for example, 2% becomes 0.02) n = the number of time periods How to calculate compound interestTo calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly: 1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042 2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24 3. Use the compound interest formula A = $2,000 x (1+ 0.0042)24A = $2,000 x 1.106 A = $2,211.64
Lorenzo and Sophia compare the compounding effect
Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term. After five years:
Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest. |
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?
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