You would like to buy a new car in five years for cash. The price of the car today is $$56,000$ and you expect that the price will increase by $6\%$ per year. You plan to save for this car starting today with a deposit in your savings account, which currently has a balance of $$1,800$ and earns $4\%$ compounded annually.

You know that you will be receiving an inheritance of $$3,500$ three years from today, which you will deposit in your savings account for the car. If you make a deposit every month for the next five years beginning one month from today, how much will the deposit have to be in order for you to be able to pay cash for the car?

Tasks:

Analyze the differences in the value of the car today and the value of the car in $3$ years. Why will this value change?

Evaluate the amount of money you will have saved and the amount needed to purchase the car. Are they the same?

Justify it would be financially smarter to purchase the car today and pay a $5\%$ interest rate, or wait and purchase the car in $5$ years.