if the compound interest on a sum for 2 years at 4% p. a. is ₹408, then the simple interest on the same sum at the same rate and for the same period is (I) ₹400 (ii) ₹398 (iii) ₹200 (iv) ₹204

Given that:

CI = ₹408

years = 2 years

Rate of interest = 4%

A = P{1+(R/100)}^

A-P = p{1+(R/100)}^n - P

I = P[1+(R/100)}^n - 1]

408 = P[{1+(4/100)²} - 1]

= P[{1+(1/25)²} - 1]

= P[(26/25)² - 1]

= P[(676/625) - 1]

= P[(676-625)/625]

408 = P(51/625)

P = 408*(625/51)

= 8*625 = 5000

Sum = 5000

Simple Interest (I) = (P*R)/100

= 5000*2*(4/100)

= 50*2*4 = 400

From the given above options, option (a) ₹400 is your correct answer.