1. **State the problem:** You want to find the time $t$ it takes for an investment of P1200 to grow to P1728 at an annual interest rate of 20% compounded annually. 2. **Use the compound interest formula:** $$A = P(1 + r)^t$$ where - $A = 1728$ (final amount), - $P = 1200$ (principal), - $r = 0.20$ (annual interest rate), - $t$ is the time in years. 3. **Substitute the given values:** $$1728 = 1200(1 + 0.20)^t$$ which simplifies to $$1728 = 1200(1.20)^t$$ 4. **Isolate $(1.20)^t$:** $$\frac{1728}{1200} = (1.20)^t$$ $$1.44 = (1.20)^t$$ 5. **Solve for $t$ using logarithms:** Take the natural logarithm on both sides: $$\ln(1.44) = \ln(1.20^t) = t \ln(1.20)$$ 6. **Calculate $t$:** $$t = \frac{\ln(1.44)}{\ln(1.20)}$$ Calculate each term: $$\ln(1.44) \approx 0.3646$$ $$\ln(1.20) \approx 0.1823$$ So $$t \approx \frac{0.3646}{0.1823} = 2$$ **Final answer:** It will take approximately **2 years** for the investment to grow to P1728 at 20% annual compound interest.