This solution explains the calculation of compound interest compounded half-yearly.
Compound Interest Calculation Steps
We need to find the compound interest on a principal amount for a given time period and interest rate, compounded half-yearly.
Given Values:
- Principal (P) = ₹2,800
- Time (T) = $1\frac{1}{2}$ years
- Annual Interest Rate (R) = 10% per annum
- Compounding Frequency = Half-yearly
Adjusting Rate and Time for Half-Yearly Compounding:
Since the interest is compounded half-yearly, we adjust the rate and time:
- Rate per period (r) = $\frac{R}{2} = \frac{10\%}{2} = 5\% = 0.05$
- Number of periods (n) = $T \times 2 = 1.5 \times 2 = 3$ periods
Calculating the Amount:
The formula for the amount (A) when compounded is:
$ A = P \left(1 + r\right)^n $Substitute the values:
$ A = 2800 \left(1 + 0.05\right)^3 $ $ A = 2800 \left(1.05\right)^3 $ $ A = 2800 \times 1.157625 $ $ A = 3241.35 $So, the total amount after $1\frac{1}{2}$ years is ₹3,241.35.
Calculating the Compound Interest:
The compound interest (CI) is the difference between the final amount and the principal amount:
$ \text{CI} = A - P $ $ \text{CI} = 3241.35 - 2800 $ $ \text{CI} = 441.35 $Final Answer:
The compound interest is ₹441.35.
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?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- 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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- 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:
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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?
