Given:
Principal amount (P) = 4000
Rate of interest (r) = 5% (half yearly)
Time period (t) = 3 years

To Find:
1. Amount (A)
2. Compound Interest (CI)

Solution:

Step 1: Calculate the half-yearly interest rate:
Given that the interest is compounded half-yearly, we need to convert the annual interest rate to a half-yearly rate.
Half-yearly interest rate (r') = r/2 = 5%/2 = 2.5%

Step 2: Calculate the number of compounding periods:
Since the time period is given in years, and the interest is compounded half-yearly, we need to calculate the number of compounding periods (n).
Number of compounding periods (n) = 2 * t = 2 * 3 = 6

Step 3: Calculate the amount:
The amount (A) can be calculated using the formula for compound interest:
A = P * (1 + r')^n

Substituting the given values:
A = 4000 * (1 + 2.5%)^6

Step 4: Calculate the compound interest:
The compound interest (CI) can be calculated by subtracting the principal amount from the amount:
CI = A - P

Step 5: Perform the calculations:
Using a calculator or spreadsheet, we can calculate the amount and compound interest:

A = 4000 * (1 + 0.025)^6 = 4000 * (1.025)^6 = 4000 * 1.159274 = 4637.10 (approximately)

CI = A - P = 4637.10 - 4000 = 637.10 (approximately)

Final Answer:
The amount after 3 years with a half-yearly interest rate of 5% is approximately Rs. 4637.10. The compound interest earned is approximately Rs. 637.10.

4000 (1+5/100)power 3_4000=630•5