The problem asks for the rate of interest (R) given the principal amount (P), time period (n), and the difference between Compound Interest (CI) and Simple Interest (SI) for 2 years.
Interest Rate Calculation: CI vs SI Difference
Given:
- Principal (P) = ₹16,000
- Time (n) = 2 years
- Difference (CI - SI) = ₹1,000
Compound vs Simple Interest Formula
For a period of 2 years, the difference between compound interest and simple interest is given by the formula:
Difference = $ P \left( \frac{R}{100} \right)^2 $
Where:
- P is the principal amount
- R is the annual rate of interest in percent
Solving for Rate of Interest
Substitute the given values into the formula:
$ 1000 = 16000 \left( \frac{R}{100} \right)^2 $
Now, we need to solve for R:
- Divide both sides by 16000: $ \frac{1000}{16000} = \left( \frac{R}{100} \right)^2 $
- Simplify the fraction: $ \frac{1}{16} = \left( \frac{R}{100} \right)^2 $
- Take the square root of both sides: $ \sqrt{\frac{1}{16}} = \frac{R}{100} $
- Calculate the square root: $ \frac{1}{4} = \frac{R}{100} $
- Solve for R: $ R = \frac{1}{4} \times 100 $ $ R = 25 $
Therefore, the rate of interest is 25% per annum.
Similar Questions
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
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The difference between the compound interest and the simple interest on a principal sum of $₹24,000$ in $2$ years at same rate of interest is $₹60$. The rate of interest is:
Important Questions from Simple and Compound Intrest
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
- Amit invested the same sum at simple and compound interest (compounded annually) for 2 years at 4% per annum. The difference between the compound interest and the simple interest is ₹47. Find the sum (in ₹) invested in each case.
- Amit invested equal amounts at simple interest and compound interest, compounded annually, for 2 years at the same rate of 4% per annum. In the end, he found a difference of ₹53 between the two interests earned. What was the amount (in ₹) invested in each case?
