Question 5: Putting all this information together, can you give a formula that would compute the amount of money earned if we invest a principle P using annual interest r over t years and we compound infinitely many times over the year? Give this formula. This is called continuously compounded interest. Compute the amount we get for investing $10,000 for 20 years at an annual rate of 0.5% and continuously compound. Discuss how you derived your formula. The above was one of many applications of limits. We will now change gears and look at limits more broadly.

QUESTION 29 On the birth of his first nephew, Donald decides he'd like to give his nephew $500 when he turns 13 years old. Donald's savings account earns 2% interest compounded monthly. How much money does Donald need to deposit now so that in 13 years he'll have $500 for his nephew? Give your answer to the nearest cent. Summarize the information provided, stating the interest rate in a decimal form. PN = r = k = N = Identify the formula you will use to solve by writing the letter of the formula here: A. A = Po(1 + rt) B. PN = Po(1 + /NK %3D C. PN = d((1 + /k) Nk – 1) + ("/k) D. Po = d(1 - (1 + /k)¬Nk) + ("/k) Solve the problem and give your answer here: