1. **State the problem:** Joe wants to save $5500 to buy a gaming PC and chair. He currently has $5225 saved and invests it at an annual interest rate of 1.75%. We need to find how long it will take for his savings to grow to $5500. 2. **Formula used:** For compound interest (assuming interest is compounded annually), the formula is: $$A = P(1 + r)^t$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (initial money). - $r$ is the annual interest rate (decimal). - $t$ is the time in years. 3. **Set up the equation:** We want $A = 5500$, $P = 5225$, and $r = 0.0175$. $$5500 = 5225(1 + 0.0175)^t$$ 4. **Isolate the exponential term:** $$\frac{5500}{5225} = (1.0175)^t$$ 5. **Simplify the fraction:** $$\frac{5500}{5225} = \frac{\cancel{5500}}{\cancel{5225}} = 1.0526$$ (approximate) 6. **Take the natural logarithm of both sides:** $$\ln(1.0526) = \ln((1.0175)^t)$$ 7. **Use logarithm power rule:** $$\ln(1.0526) = t \ln(1.0175)$$ 8. **Solve for $t$:** $$t = \frac{\ln(1.0526)}{\ln(1.0175)}$$ 9. **Calculate the values:** $$\ln(1.0526) \approx 0.0513$$ $$\ln(1.0175) \approx 0.0173$$ 10. **Final calculation:** $$t = \frac{0.0513}{0.0173} \approx 2.97$$ years **Answer:** It will take Joe approximately 2.97 years to have enough money to make his purchase and stop getting cooked online.