Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
The problem asks for the compound interest calculated on a principal amount, compounded half-yearly.
Principal and Rate Adjustment
The principal amount (P) is ₹8,000.
The annual interest rate (R) is 10%.
Since interest is compounded half-yearly, the rate per period (r) is:
$r = \frac{R}{2} = \frac{10\%}{2} = 5\% = 0.05$
Time Period Adjustment
The time period (T) is $1\frac{1}{2}$ years, which is 1.5 years.
For half-yearly compounding, the number of periods (n) is:
$n = T \times 2 = 1.5 \times 2 = 3$ periods
Compound Amount Calculation
The formula for the compound amount (A) is $A = P \times (1 + r)^n$.
Substituting the values:
$A = 8000 \times (1 + 0.05)^3$
$A = 8000 \times (1.05)^3$
$A = 8000 \times 1.157625$
$A = 9261$
Compound Interest Calculation
The compound interest (CI) is the difference between the final amount and the principal amount:
$CI = A - P$
$CI = 9261 - 8000$
$CI = 1261$
Final Answer
The compound interest is ₹1,261.
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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 ₹______.
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