Problem 3 (2p) a) A principal of $50 000 is invested at an annual interest rate of 4 %. In case the interest is compounded continous, how long time do you need in order to double the principal? b) If you want to double the principal in ten years (still compounded continous), what annual interest rate do you need? Problem 4 (2 p) An individual saves $500 in a bank account at the beginning of each year for 50 years. No further savings or withdrawals are made from the account. Determine the total amount saved if the annual interest rate is 4%, compounded quarterly. That is; how much money is there at the account at the end of the 50th year