An antique automobile is depreciating, i.e. losing value i.e. going down in price at a rate of 7% per annum compounded annually. Betty and Bob have an account, which earns interest at a rate of 12% per annum continuously compounded. They originally had $9,000 in the account and withdrew $2000 after the second year and $2,500 after the third year. They had enough money (exactly) to buy the automobile after 6 years. Algebraically find the original value of the automobile.

(I need a step-by-step explanation of the formulas used. Thanks)