Question:
At what rate percent a sum of rupees 5000 produce rupees 408 as compound interest 5% per annum?

Solution:
To determine the rate percent at which a sum of rupees 5000 produces rupees 408 as compound interest, we need to use the compound interest formula:

Compound Interest Formula:
A = P(1 + R/100)^T

Where:
A = Total amount after interest
P = Principal amount (initial sum)
R = Rate of interest per annum
T = Time period in years

In this case, the principal amount (P) is rupees 5000, the compound interest (A) is rupees 408, and the rate of interest per annum (R) is unknown. We are given that the time period (T) is 1 year and the rate of interest (R) is 5% per annum.

Step 1: Substitute the given values into the compound interest formula:
408 = 5000(1 + R/100)^1

Step 2: Solve the equation for the unknown rate (R):
(1 + R/100)^1 = 408/5000
(1 + R/100) = (408/5000)^(1/1)
1 + R/100 = 0.0816
R/100 = 0.0816 - 1
R/100 = -0.9184
R = -0.9184 * 100
R = -91.84

Step 3: Interpret the rate percent:
The negative rate (-91.84) does not make sense in the context of compound interest. It indicates a decrease in the principal amount, which is not possible. Therefore, there is no rate percent at which a sum of rupees 5000 produces rupees 408 as compound interest with a 5% per annum interest rate.

Conclusion:
There is no rate percent at which a sum of rupees 5000 produces rupees 408 as compound interest with a 5% per annum interest rate.