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
- If the interest earned during the $2^{\text{nd}}$ year on a certain sum is ₹6,258, and the rate of interest is 20% per annum compounded annually, then the sum is:
- The difference between compound interest and simple interest, at the same rate, on an amount of ₹15,000 for 2 years is ₹24. What is the rate of interest per annum?
- 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?
- Simple interest on a sum of money, at $5\%$ per annum for 2 years, is ₹50. The compound interest on the same sum for the same period at the same interest rate is:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
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- 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:
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Important Questions from Simple and Compound Intrest
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
