Please show all work. Thank you! Correct answer should be $46,641.

5. An account pays interest at a continuously compounded rate of 4% per year. Continuous deposits are made to the account at a rate of 2,000 per year for 10 years, and then at a rate of 3,000 per year for the next 5 years. Calculate the account balance at the end of 15 years. 5. An account pays interest at a continuously compounded rate of 4% per year. Continuous deposits are made to the account at a rate of 2,000 per year for 10 years, and then at a rate of 3,000 per year for the next 5 years. Calculate the account balance at the end of 15 years