RRB ALP practice question
Ashok borrowed ₹15,000 for 2 years 8 months. The loan carries compound interest at 8% per annum (compounded annually) for the first 2 years; for the remaining 8 months, simple interest at 6% per annum is charged on the amount outstanding at the end of 2 years. Find the compound interest he pays for the entire period.
From a RRB ALP Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (D) ₹3,195.84
Here the rate changes at the fractional boundary: 8% per annum (compounded annually) applies for the first 2 whole years, and 6% per annum simple interest applies only on the amount outstanding, for the remaining 8 months.
Step 1: Amount after 2 years at 8% compound interest = ₹15000 × (1+8/100)2 = ₹15000 × 1.1664 = ₹17,496.
Step 2: Simple interest for the remaining 8 months (= 2/3 year) at 6% p.a. on ₹17,496 = (17,496 × 6 × 2/3) / 100 = ₹699.84.
Step 3: Final amount = ₹17,496 + ₹699.84 = ₹18,195.84.
Compound interest = ₹18,195.84 − ₹15000 = ₹3,195.84.
∴ The required compound interest = ₹3,195.84.
Step 1: Amount after 2 years at 8% compound interest = ₹15000 × (1+8/100)2 = ₹15000 × 1.1664 = ₹17,496.
Step 2: Simple interest for the remaining 8 months (= 2/3 year) at 6% p.a. on ₹17,496 = (17,496 × 6 × 2/3) / 100 = ₹699.84.
Step 3: Final amount = ₹17,496 + ₹699.84 = ₹18,195.84.
Compound interest = ₹18,195.84 − ₹15000 = ₹3,195.84.
∴ The required compound interest = ₹3,195.84.
हिंदी में प्रश्न
अशोक ने 2 वर्ष 8 माह के लिए ₹15,000 उधार लिए। पहले 2 वर्षों के लिए ऋण पर 8% वार्षिक दर से चक्रवृद्धि ब्याज (प्रतिवर्ष चक्रवृद्धि) लगता है; शेष 8 माह के लिए, 2 वर्षों के अंत में शेष राशि पर 6% वार्षिक दर से केवल साधारण ब्याज लगता है। पूरी अवधि के लिए उसके द्वारा चुकाया गया चक्रवृद्धि ब्याज ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (D) ₹3,195.84
यहाँ भिन्नात्मक सीमा पर ब्याज दर बदल जाती है: पहले पूरे 2 वर्ष के लिए 8% वार्षिक दर से चक्रवृद्धि ब्याज (प्रतिवर्ष चक्रवृद्धि) लगेगा, तथा शेष 8 माह के लिए उस समय तक की मिश्रधन राशि पर 6% वार्षिक दर से केवल साधारण ब्याज लगेगा।
चरण 1: 2 वर्ष बाद 8% चक्रवृद्धि ब्याज से मिश्रधन = ₹15000 × (1+8/100)2 = ₹15000 × 1.1664 = ₹17,496।
चरण 2: शेष 8 माह (= वर्ष का 2/3 भाग) के लिए ₹17,496 पर 6% वार्षिक दर से साधारण ब्याज = (17,496 × 6 × 2/3) / 100 = ₹699.84।
चरण 3: अंतिम मिश्रधन = ₹17,496 + ₹699.84 = ₹18,195.84।
चक्रवृद्धि ब्याज = ₹18,195.84 − ₹15000 = ₹3,195.84।
∴ अभीष्ट चक्रवृद्धि ब्याज = ₹3,195.84 है।
चरण 1: 2 वर्ष बाद 8% चक्रवृद्धि ब्याज से मिश्रधन = ₹15000 × (1+8/100)2 = ₹15000 × 1.1664 = ₹17,496।
चरण 2: शेष 8 माह (= वर्ष का 2/3 भाग) के लिए ₹17,496 पर 6% वार्षिक दर से साधारण ब्याज = (17,496 × 6 × 2/3) / 100 = ₹699.84।
चरण 3: अंतिम मिश्रधन = ₹17,496 + ₹699.84 = ₹18,195.84।
चक्रवृद्धि ब्याज = ₹18,195.84 − ₹15000 = ₹3,195.84।
∴ अभीष्ट चक्रवृद्धि ब्याज = ₹3,195.84 है।
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