Understanding Compound Interest
To calculate the amount of a sum when compounded semi-annually, we will use the formula for compound interest:
Amount (A) = P(1 + r/n)^(nt)
Where:
- P = Principal amount
- r = Annual interest rate (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
Given Values
- Principal (P) = 24000
- Annual interest rate (r) = 10% = 0.10
- Number of times compounded per year (n) = 2
- Time (t) = 2 years
Step-by-Step Calculation
- First, substitute the values into the formula:
A = 24000 * (1 + 0.10/2)^(2*2)
- Calculate the interest rate per period:
r/n = 0.10/2 = 0.05
- Calculate the number of compounding periods:
nt = 2 * 2 = 4
- Now, substitute these values:
A = 24000 * (1 + 0.05)^(4)
A = 24000 * (1.05)^(4)
- Calculate (1.05)^4:
(1.05)^4 ≈ 1.21550625
- Now complete the calculation:
A ≈ 24000 * 1.21550625 ≈ 29172.15
Final Amount
After 2 years, a sum of rupees 24000 will amount to approximately Rs. 29172.15 at 10% per annum compounded semi-annually. This demonstrates the power of compound interest over time!