Question

The compound interest on a certain sum of money for 2 year at 5% is 328, then the sum is?

Answer 1

Let,

Principal = P

Interest rate = r% p.a. compounded annually

Interest = I

Amount = A= P+I

Compounding No. = n i.e. no. of times in a year interest is calculated

Time = t = expressed in no. of years

As per C.I. formula

A = P.( 1+r%/n)^(nt)

I = A- P

= P.( 1+r%/n)^(nt) -P

= P[ (1+r%/n)^(nt) -1] = 328

or, P [ (1+5/100/1)^1*2 -1] = 328

or, P [ (1.05)^2 -1] =328

or, P [ (1.05)^2 -1^2] = 328

or, P [ (1.05+1)*(1.05-1)]=328 (by applying a^2-b^2= (a+b)(a-b) formula)

or, P (2.05*.05) = 328

or, P (0.1025) = 328

or P= 328/.1025 = Rs. 3200

Hence, principal was Rs. 3200