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
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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).
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- 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 ₹______.
