On a certain sum, C.I. is Rs 41 and SI is Rs 40. for 2 years. What is the rate p.a.

To find the rate per annum (p.a.), we need to calculate the rate of interest.

The formula for simple interest (SI) is given by:

SI = (Principal × Rate × Time) / 100

In this case, we know that the SI is Rs 40, the time is 2 years, and the principal amount is not given explicitly.

To calculate the principal amount, we can use the formula for compound interest (CI):

CI = Principal × [(1 + Rate/100) ^ Time] - Principal

We are given that the CI is Rs 41 for 2 years, so we can write the equation as follows:

41 = Principal × [(1 + (Rate/100)) ^ 2] - Principal

Now, let's solve for the principal by rearranging the equation:

Principal × [(1 + (Rate/100)) ^ 2] = 41 + Principal

Dividing throughout by the principal, we get:

[(1 + (Rate/100)) ^ 2] = (41 + Principal) / Principal

Now, using the given information that the SI is Rs 40 for 2 years, we can calculate the principal:

SI = (Principal × Rate × Time) / 100
40 = (Principal × Rate × 2) / 100
40 = Principal × Rate / 50
Rate = (40 × 50) / Principal

We now have two equations:

1. [(1 + (Rate/100)) ^ 2] = (41 + Principal) / Principal
2. Rate = (40 × 50) / Principal

By solving these two equations simultaneously, we can find the rate per annum (p.a.). Unfortunately, without the value of the principal amount or additional information, we cannot determine the exact rate.