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Question

# A certain sum amount to ₹5292 in two years and ₹5556.60 in three years interest being compounded annually. Find the rate of interest and the original sum

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Solution

## Given amount of 2 years = 5292 Rs Amount of 3 years = Rs 5556.6. Let sum = Rs p and rate of interst = r% Amount = sum (1+rate/100)^time 5292 = p (1+r/100)² p = 5292/(1+r/100)² → A Similarly 5556.60 = p(1+r/100)³ p = 5556.60/(1+r/100)³ → B From A and B 5292/(1+r/100)² = 5556.60/(1+r100)³ 5292 = 5556.60/(1+r/100) 5292 = 5556.60/(100+r/100) 5292 = 5556.60*100/(100+r) 529200 + 5292r = 555660 5292r = 555660 - 529200 r = 26460/5292 = 5% Rate of interest = 5% p = 5292/(1+5/100)² p = 5292/(21/20)² p = 5292/(441/400) p = 5292*400/441 = Rs 4800 Sum = Rs 4800 Like if satisfied

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