On what sum will the compound interest for 2 years at 4% per annum be ₹ 5712?
Solution:
It is given that
CI = ₹ 5712
Rate of interest (r) = 4% p.a.
Period (n) = 2 years
We know that
A = P (1 + r/100)n
It can be written as
CI = A – P = P (1 + r/100)n – P
= P [(1 + r/100)n – 1]
Substituting the values
5712 = P [(1 + 4/100)2 – 1]
= P [(26/25)2 – 1]
By further calculation
= P [676/625 – 1]
Taking LCM
= P [(676 – 625)/ 625]
= P × 51/625
Here
P = 5712 × 625/51
= 112 × 625
= ₹ 70000
Hence, the principal amount is ₹ 70000.
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