Problem 6: 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 $8,000 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 5 years. Algebraically find the original value of the automobile. Your final answer should be correct to 2 places after the decimal point