The difference between simple and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is ₹1. The value of principal amount is _____.
₹625
Let the sum be ₹x.
Amount after 2 years on ₹x at 4% per annum when interest is compounded annually
=x(1+4100)2=x(104100)2
Compound Interest =x(104100)2−x
=x[(104100)2−1] = x[(2625)2−1] = x[676625−1] = x[51625]=51x625
Simple Interest =PRT100=x×4×2100=2x25
Given that difference between compound interest and simple interest is ₹1.
⇒51x625−2x25=1
⇒51x−50x625=1
⇒x=625
∴ the principal amount is ₹625.