Find the difference between the simple interest and compound interest on ₹ 2500 for 2 years at 4% per annum, compound interest being reckoned semi-annually.
Solution:
It is given that
Principal (P) = ₹ 2500
Rate of interest (r) = 4% p.a. or 2% half-yearly
Period (n) = 2 years or 4 half-years
We know that
SI = Prt/100
Substituting the values
= (2500 × 4 × 2)/100
= ₹ 200
If compounded semi-annually
A = P (1 + r/100)n
Substituting the values
= 2500 (1 + 2/100)4
By further calculation
= 2500 × 51/50 × 51/50 × 51/50 × 51/50
= ₹ 2706.08
We know that
CI = A – P
Substituting the values
= 2706.08 – 2500
= ₹ 206.08
So the difference between CI and SI = 206.08 – 200 = ₹ 6.08
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