1. **Problem statement:** A sum of money doubles itself in 3 years at compound interest. We need to find in how many years it will amount to 64 times the original sum. 2. **Formula used:** The amount $A$ after $n$ years at compound interest rate $r$ is given by: $$A = P(1 + r)^n$$ where $P$ is the principal. 3. Since the sum doubles in 3 years, we have: $$2P = P(1 + r)^3 \implies (1 + r)^3 = 2$$ 4. We want to find $n$ such that: $$P(1 + r)^n = 64P \implies (1 + r)^n = 64$$ 5. Using the relation from step 3, substitute $(1 + r)^3 = 2$: $$ (1 + r)^n = ((1 + r)^3)^{\frac{n}{3}} = 2^{\frac{n}{3}} = 64$$ 6. Since $64 = 2^6$, we get: $$2^{\frac{n}{3}} = 2^6 \implies \frac{n}{3} = 6 \implies n = 18$$ 7. **Answer:** It will take **18 years** for the sum to amount to 64 times. This corresponds to option (a).