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
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