Part II: Joe and his Dream Porsche Joe is 16 years old and has decided that he wants a brand-spankin' new Porsche Boxter Convertible, but his mom says there's no way that he could ever afford it! So, Joe has decided to show his mom that he will be able to purchase his dream car at the age of 35 if he plans his finances just right. He's asked you to help him plan. A. How much will his car cost in 19 years? The following table shows the approximate MSRP (manufacturers suggested retail price) of a Porsche Boxter Convertible from 2004 to 2008. Create a scatter plot of the data and determine the line of best fit, finding an appropriate slope and initial value assuming it started in 2004.. Year MSRP 2004 $57 510 2005 $59 130 2006 $60 750 2007 $61 965 2008 $63 600 B. Financing Joe's new Porsche Joe knows that he will have to put 10% down on his car. To save up for this down payment, he plans on investing a set amount monthly, starting now, into Teen's Choice Financial's Interest Plus Savings Account which pays 4% compounded monthly. C. Mom says: Don't forget Insurance! Joe's mom says that he'll have to pay outrageous insurance rates on a Porsche. Joe has been told that insurance rates are dependent upon the driver's age. His driver's training instructor gave Joe the following table to help him out. It shows insurance rates for a male Porsche driver with a perfect driving record based on different ages. Annual Insurance Driver's Age Rate 18 $5 575.30 19 $5 296.54 20 $5 031.71 21 $4 780.12 22 $4 541.12 23 $4 314.06 1. Scatter Plot and Line of Best Fit: • Data: The table provides the MSRP (Manufacturer's Suggested Retail Price) of a Porsche Boxster Convertible from 2004 to 2008. • Scatter Plot: Plot the given data points (Year, MSRP) on a graph. • Line of Best Fit: Visually fit a straight line. through the data points that best represents the trend. This line represents the linear relationship between the year and the MSRP. 2. Equation of the Line: • Slope: Calculate the slope of the line using the formula: Slope (m) = (Change in MSRP) / (Change • Initial Value: Find the MSRP value (y- intercept) when the year is 2004. This is the initial value (b) in the equation. • Equation: The equation of the line will be in the form: MSRP = m * Year + b 3. MSRP in 19 Years: • Year: Joe is 16 now, so in 19 years, he will be 35. • Calculation: Substitute the year (35) into the equation to find the predicted MSRP. B. Financing Joe's New Porsche a. Down Payment: • Calculation: 10% of the MSRP calculated in part A. b. Monthly Savings: • TVM Solver: Use a financial calculator or software with a TVM (Time Value of Money) solver. . Inputs: • PV (Present Value) = 0 (starting amount) • FV (Future Value) = Down Payment amount 。 N (Number of periods) = 19 years * 12 months/year = 228 months ○ I/Y (Interest rate per year) = 4% (annual interest rate) 。 P/Y and C/Y (Payments per year and Compounding periods per year) = 12 • Solve for PMT (Monthly Payment): Calculate the monthly deposit required. c. Monthly Car Payments: • TVM Solver: Use the TVM solver again. • Inputs: 。 PV (Present Value) = MSRP - Down Payment • FV (Future Value) = 0 (loan will be paid off) ○ N (Number of periods) = 84 months • I/Y (Interest rate per year) = 8.2% (annual interest rate) 。 P/Y and C/Y (Payments per year and Compounding periods per year) = 12 • Solve for PMT (Monthly Payment): Calculate the monthly car payment. C. Mom Says: Don't Forget Insurance! a. Equation of Best Fit: • Linear Regression: Use a statistical software or calculator to perform linear regression on the driver's age and annual insurance rate data. This will provide the equation of the best-fit line. b. Insurance Rate at Age 35: • Substitute Age: Plug Joe's age (35) into the equation to find the predicted annual insurance rate. c. Total Monthly Costs: • Calculate: Add the monthly car payment and the monthly insurance payment (annual insurance rate divided by 12). d. Should Joe Rethink? Analyze Costs: Consider the total monthly • cost and Joe's financial situation. If the cost is too high, he might need to reconsider buying a Porsche.