1. **Problem 1: Inflation and Car Cost** The problem asks: If inflation causes the cost of automobiles to increase by 2.5% each year, what should a car cost today if it cost 21000 five years ago? 2. **Formula:** The formula for future value with inflation is: $$\text{Future Value} = \text{Past Value} \times (1 + r)^t$$ where $r$ is the inflation rate (as a decimal), and $t$ is the number of years. 3. **Calculation:** Given $r = 0.025$, $t = 5$, and past value = 21000, $$\text{Future Value} = 21000 \times (1 + 0.025)^5 = 21000 \times 1.131408 = 23759.57$$ 4. **Answer:** The car should cost approximately $23759.57 today. --- 5. **Problem 2: Effective Annual Interest Rate** The problem asks: What is the effective annual interest rate of an investment paying 6.5% annual interest compounded daily (365 days)? 6. **Formula:** $$\text{Effective Annual Rate (EAR)} = \left(1 + \frac{r}{n}\right)^n - 1$$ where $r$ is the nominal annual rate, and $n$ is the number of compounding periods per year. 7. **Calculation:** Given $r = 0.065$, $n = 365$, $$EAR = \left(1 + \frac{0.065}{365}\right)^{365} - 1 = (1.00017808)^{365} - 1 \approx 0.0672 = 6.72\%$$ 8. **Answer:** The effective annual interest rate is approximately 6.72%. --- 9. **Problem 3: Probability of Drawing 3 White Balls** The problem asks: From a box with 5 red, 8 black, and 4 white balls, what is the probability that all three drawn balls are white? 10. **Total balls:** $$5 + 8 + 4 = 17$$ 11. **Probability formula for drawing 3 white balls without replacement:** $$P = \frac{\binom{4}{3}}{\binom{17}{3}}$$ 12. **Calculate combinations:** $$\binom{4}{3} = 4$$ $$\binom{17}{3} = \frac{17 \times 16 \times 15}{3 \times 2 \times 1} = 680$$ 13. **Calculate probability:** $$P = \frac{4}{680} = 0.00588 \approx 0.0059$$ 14. **Answer:** The probability that all three balls drawn are white is approximately 0.0059.