Time value Personal Finance Problem As part of your financial planning, you wish to purchase a new car $7$ years from today. The car you wish to purchase costs $$15,000$ today, and your research indicates that its price will increase by $3\%$ to $6\%$ per year over the next $7$ years.

a$.$ Estimate the price of the car at the end of $7$ years if inflation is $(1)3\%$ per year and $(2)6\%$ per year.

b$.$ How much more expensive will the car be if the rate of inflation is $6\%$ rather than $3\%?$

c$.$ Estimate the price of the car if inflation is $3\%$ for the next $3$ years and $6\%$ for $4$ years after that.

a$.$ The price of the car at the end of $7$ years, if inflation is $3\%$ per year, is $ $($Round to the nearest cent.$)$