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

Answer 1

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


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