If a sum of ₹ 2000 is lent at 10% p.a. compound interest, what is the interest for the second year?
₹220
Let's analyze the question about calculating the interest for the second year on a sum of ₹ 2000 at 10% p.a. compound interest.
Understanding Compound Interest Calculation
Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. This means that the principal amount grows over time, leading to higher interest earnings in subsequent periods compared to simple interest.
To find the interest for the second year specifically, we first need to determine the amount at the end of the first year. This amount then becomes the principal for calculating the interest in the second year.
Step-by-Step Calculation of Second Year Interest
Here's how we can calculate the interest earned only during the second year:
- Identify the initial principal amount, the interest rate, and the time period for the first year.
- Calculate the interest for the first year. Since it's compound interest, the interest for the first year is the same as simple interest on the initial principal.
- Add the interest for the first year to the initial principal to find the amount at the end of the first year. This amount is the principal for the second year.
- Calculate the interest for the second year using the amount at the end of the first year as the new principal and the given interest rate for one year (the second year).
Calculation Details:
- Initial Principal (P) = ₹ 2000
- Annual Interest Rate (R) = 10% p.a.
Step 1 & 2: Calculate Interest for the First Year
Interest for the 1st year = \( \frac{P \times R \times 1}{100} \)
Interest for the 1st year = \( \frac{2000 \times 10 \times 1}{100} \)
Interest for the 1st year = \( \frac{20000}{100} \)
Interest for the 1st year = ₹ 200
Step 3: Calculate Amount at the end of the First Year
Amount at end of 1st year = Initial Principal + Interest for 1st year
Amount at end of 1st year = ₹ 2000 + ₹ 200
Amount at end of 1st year = ₹ 2200
This amount (₹ 2200) becomes the principal for the second year.
Step 4: Calculate Interest for the Second Year
Principal for the 2nd year = ₹ 2200
Interest Rate for 2nd year = 10% p.a.
Interest for the 2nd year = \( \frac{\text{Principal for 2nd year} \times R \times 1}{100} \)
Interest for the 2nd year = \( \frac{2200 \times 10 \times 1}{100} \)
Interest for the 2nd year = \( \frac{22000}{100} \)
Interest for the 2nd year = ₹ 220
Thus, the interest earned during the second year is ₹ 220.
| Period | Starting Principal | Interest Rate | Interest Earned | Ending Amount |
|---|---|---|---|---|
| 1st Year | ₹ 2000 | 10% | \( \frac{2000 \times 10}{100} = \) ₹ 200 | \( 2000 + 200 = \) ₹ 2200 |
| 2nd Year | ₹ 2200 | 10% | \( \frac{2200 \times 10}{100} = \) ₹ 220 | \( 2200 + 220 = \) ₹ 2420 |
Revision Table: Compound Interest Basics
| Term | Definition | Formula (Annual Compounding) |
|---|---|---|
| Principal (P) | The initial amount of money invested or borrowed. | N/A |
| Rate (R) | The percentage at which interest is charged per period (usually per year). | N/A |
| Time (n or t) | The duration for which the money is invested or borrowed. | N/A |
| Amount (A) | The total sum at the end of the time period, including principal and interest. | \( A = P(1 + \frac{R}{100})^n \) |
| Compound Interest (CI) | The interest calculated on the principal and accumulated interest. | \( CI = A - P \) or \( CI = P((1 + \frac{R}{100})^n - 1) \) |
Additional Information: Types of Interest
Interest is the cost of borrowing money or the return for lending money. There are two primary types:
- Simple Interest (SI): Calculated only on the initial principal amount for the entire duration. The interest earned does not add to the principal for calculating future interest.
- Compound Interest (CI): Calculated on the initial principal and the accumulated interest from previous periods. This leads to exponential growth in the amount over time, assuming a positive interest rate.
The key difference lies in how the interest is calculated in subsequent periods. Simple interest uses the original principal, while compound interest uses the updated principal (original principal + accumulated interest).
Important Questions from Compound Interest
The certain sum amounts to Rs. 9,982.50 in \(2\frac{1}{2}\) years at 12% p.a., interest compounded 10-monthly. The sum (in Rs.) is:
The difference between the simple interest and the compound interest compounded annually on a certain sum of money for 2 years at a rate of 8% per annum is Rs. 16.80. Find the principle amount.
A sum becomes 5 times of itself in 3 years. at compound interest (interest is compounded annually). In how many years. will the sum becomes 125 times of itself?
If the compound interest on a certain sum of money for two years at 9% p.a. is Rs. 3,762, then the sum is:
The compound interest on a sum of ₹ 24500 at 10% p.a for \(2\frac{2}{5}\) years interest compounded yearly is:
