The compound interest on a certain sum of money for 2 years at 5% per annum is 410. The simple interest on the same sum at the same rate and for the same time is

we know that :

1. For first year , compound interest and simple interest is same if the principal amount and rate of interest is same in both cases.

2. From 2nd year onwards ,the compound interest is normal interest plus the interest on accumulated amount due to interest untill last cycle.

3. Every year simple interest remains same if Rate of Interest and principal amount remains same .

Let the compound interest for 1st year be be Rs y

For two years ,CI = Rs 410

y + y + $$\frac{5}{100}$$y = 410

$$\frac{41y}{20}$$ = 410

y = 200

So for two years , Simple Interest = 200 + 200 = Rs 400