1. **State the problem:** The principal amount becomes 5 times in 12 years. We want to find how many times the principal will become in 27 years. 2. **Understand the problem:** The problem is describing exponential growth of the principal. Let the principal be $P$. After 12 years, the amount is $5P$. We want to find the amount after 27 years. 3. **Mathematical model:** Assume the growth follows compound interest formula or exponential model: $$A = P \times r^t$$ where $r$ is the growth rate per year and $t$ is the time in years. Since the principal becomes 5 times in 12 years, we have: $$5P = P \times r^{12} \implies r^{12} = 5$$ 4. **Find growth rate per year:** $$r = 5^{\frac{1}{12}}$$ 5. **Calculate amount after 27 years:** $$A = P \times r^{27} = P \times \left(5^{\frac{1}{12}}\right)^{27} = P \times 5^{\frac{27}{12}} = P \times 5^{2.25}$$ 6. **Simplify exponent:** $$5^{2.25} = 5^{2 + 0.25} = 5^2 \times 5^{0.25} = 25 \times 5^{0.25}$$ 7. **Calculate $5^{0.25}$** (4th root of 5): approximately $5^{0.25} \approx 1.495$ 8. **Final calculation:** $$A = 25 \times 1.495 = 37.375$$ So after 27 years, the principal becomes approximately 37.375 times. 9. **Compare with options:** a)18 b)10 c)20 d)13 None exactly matches 37.375. Possibly problem expects closest approximation or double check. 10. **Conclusion:** Principal becomes approximately 37.375 times in 27 years; none of the options a,b,c,d matches. If the question intends compound interest or simple interest differently, the answer varies. But according to exponential growth, answer is about 37.375 times. Since none matches, possibly the question or options have a typo or expect a different interpretation. **Final answer:** approximately $37.375$ times.