Multiple choice

The difference between the simple and the compound interest compounded every six months at the rate of 20 per cent per annum at the end of 1 1 2 years is Rs.248. What is the sum? 20 प्रतिशत वार्षिक ब्याज की दर से 1 1 2 वर्षों के अंत में साधारण ब्याज तथा चक्रवृद्धि ब्याज के बीच अंतर रु.248 है, यदि ब्याज प्रत्येक छः माह में संयोजित होता है । राशि क्या है ?

  1. Rs.10000

  2. Rs.6000

  3. Rs.12000

  4. Rs.8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For half-yearly compounding, rate = 10% per period for 3 periods. CI factor = 1.1³ = 1.331. SI for 1.5 years at 20% = 1 + 0.2×1.5 = 1.3. Difference: 1.331P - 1.3P = 0.031P = 248. So P = 248/0.031 = 8000. Key insight: CI compounded half-yearly means rate/2 for 2×time periods.

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