If a certain sum becomes 4 times in a 8 years at compound interest. Then in how many years, it will become 256 times?

If sum becomes 4 times in 8 years, then 4 = (1 + R)^8, so (1+R) = 4^(1/8) = 2^(1/4) = √√2. To become 256 times: 256 = (1+R)^n = 2^(n/4). Since 256 = 2^8, we get n/4 = 8, so n = 32 years. Alternatively: 4 times in 8 years means doubling every 4 years (since 2^2 = 4). To reach 256 = 2^8, we need 8 doublings, which takes 8 × 4 = 32 years.