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**james_bond** Q1. 1st year: $\displaystyle 500\cdot 1.05$, 2nd year: $\displaystyle (500\cdot 1.05)\cdot 1.05$, etc. So $\displaystyle n$th year: $\displaystyle 500\cdot (1.05)^n$, therefore this should hold: $\displaystyle 500\cdot (1.05)^n\ge 750\leftrightarrow (1.05)^n\ge 1.5$. Take the logarithm of both sides (base 1.05, you can without reversing the sign, because it is greater than 1): $\displaystyle \log_{1.05}(1.05)^n\ge \log_{1.05}1.5$ by definition it is: $\displaystyle n\ge\log_{1.05}1.5\approx 8.31039$. So the first integer after...

Q2. Using the same idea: end of 10th year: $\displaystyle 50\cdot (1.04)^{10}=1446.27$