Introduction:
To find the principal that yields a simple interest of Rs. 40/- or a compound interest of Rs. 41/- at the same rate of interest per annum in 2 years, we need to use the formula for simple interest and compound interest respectively.

Formula for Simple Interest:
Simple Interest = (P*R*T)/100

Formula for Compound Interest:
Compound Interest = P*(1+(R/100))^T - P

Calculation for Simple Interest:
Given, Simple Interest = Rs. 40/-, Time = 2 years
Let, Rate of Interest = R% and Principal = P

Using the formula of Simple Interest,
40 = (P*R*2)/100
P*R = 2000/R

Calculation for Compound Interest:
Given, Compound Interest = Rs. 41/-, Time = 2 years
Let, Rate of Interest = R% and Principal = P

Using the formula of Compound Interest,
41 = P*(1+(R/100))^2 - P
41 = P*((1+(R/100))^2 - 1)
(1+(R/100))^2 = (41/P)+1
1+(R/100) = sqrt((41/P)+1)
R = (sqrt((41/P)+1)-1)*100

Solution:
Now, we can equate the two equations obtained for P*R and R and solve for P.

P*R = 2000/R
(sqrt((41/P)+1)-1)*100 = R

On solving, we get P = Rs. 4000/-. Therefore, the principal that yields a simple interest of Rs. 40/- or a compound interest of Rs. 41/- at the same rate of interest per annum in 2 years is Rs. 4000/-.

Explanation:
The solution is obtained by using the formulas of Simple Interest and Compound Interest and equating the two equations obtained. The value of Principal is calculated by solving the equations for Rate of Interest and Principal. The final answer is obtained as Rs. 4000/-.

400