problem with solving Compound interest?

Question

An amount is invested at $33.33\%$ compounded annually. What is the ratio of Compound interest for $4$ and $3$ years?
My approach: The fractional increment in each year is $\frac{4}{3}$. For 4 years the fraction will be $\frac{256}{81}$ and the difference between the numerator and denominator will be the compound interest i.e 175. Similarly for 3 years the fraction will be $\frac{64}{27}$ and the difference will be 37. Hence the Ratio of Compound interest for 4 and 3 years will be $175:37$. However, the answer is $175:111$, but I can't figure out how this method is giving wrong answer.

Answer 1

Make the denominator the same for the two settings:

$$256 - 81 = 175$$

$$64(3)-27(3)=37(3)=111$$