If the compound interest and simple interest of a certain sum of money for 2 years is ₹840 and ₹800 respectively, find the rate of compound interest and principle.
Understand the Problem
The question is asking to find the rate of compound interest and the principle amount, given the compound interest (CI) and simple interest (SI) of a certain sum of money for 2 years. The image also shows a method to find the rate.
Answer
Rate = $10\%$ Principal = $4000$
Answer for screen readers
Rate of Compound Interest = $10%$ Principal Amount = $4000$
Steps to Solve
- Identify the given values
Compound Interest (CI) = $840$ Simple Interest (SI) = $800$ Time = $2$ years
- Calculate the Simple Interest for 1 year
Since Simple Interest is the same each year, for 2 years it is $800$, then for one year it is $SI_{1} = \frac{800}{2} = 400$
- Calculate the difference between CI and SI
The difference between the Compound Interest and Simple Interest for 2 years is the interest on the first year's interest. $Difference = CI - SI = 840 - 800 = 40$
- Calculate the rate of interest
The rate of interest can be calculated using the formula: $Rate = \frac{Difference}{SI_{1}} \times 100$ $Rate = \frac{40}{400} \times 100 = 10%$
- Calculate the Principal The Simple Interest for 1 year is given by: $SI_{1} = \frac{P \times R \times T}{100}$, where P is the principal, R is the rate, and T is time
Since we calculated $SI_{1}$ we know that: $400 = \frac{P \times 10 \times 1}{100}$ $P = \frac{400 \times 100}{10}$ $P = 4000$
Rate of Compound Interest = $10%$ Principal Amount = $4000$
More Information
The rate of compound interest is 10% per annum, and the principal amount is $4000. This means that every year, the interest earned is 10% of the principal, and in the case of compound interest, the interest earned in previous years also earns interest.
Tips
A common mistake is to confuse simple and compound interest, and not understanding that the difference between them over 2 years is the interest earned on the first year's interest. Another mistake is making an error when performing the calculations.
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