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.
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
- A sum of money was lent on compound interest. It became ₹500 at the end of the first year and ₹550 at the end of second year. Find the rate of compound interest per annum.
- 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:
- If a sum on compound interest becomes 4 times in 3 years, then with the same interest rate, the sum will become 64 times in:
- If the difference between the compound interest and the simple interest on a certain sum of money at 8 % p.a. for 2 years is ₹240, then the sum of money is:
- The compound interest on a sum of ₹7,500 for 2 years at 4 % p.a. is
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
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- 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:
