Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the…
2024
Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest being compounded half-yearly.
- A.
Rs 1648.64
- B.
Rs 1638.64
- C.
Rs 1658.64
- D.
Rs 1618.64
Attempted by 22 students.
Show answer & explanation
Correct answer: A
Solution: Find the compound interest step by step.
Step 1: Compute the rate per half-year: 4% per annum compounded half-yearly ⇒ rate per period = 4% ÷ 2 = 2% = 0.02.
Step 2: Compute the number of half-year periods in 2 years: 2 × 2 = 4.
Step 3: Use the compound interest formula for the amount: Amount = Principal × (1 + rate per period)^(number of periods) = 20000 × (1.02)^4.
Step 4: Evaluate numerically: (1.02)^4 = 1.08243216, so Amount = 20000 × 1.08243216 = 21648.6432.
Step 5: Compound interest = Amount − Principal = 21648.6432 − 20000 = 1648.6432 ≈ Rs 1648.64.
Answer: Rs 1648.64