This exercise investigates the continuouscompounding formula, using a realistic

Chapter 5, Problem 38

(choose chapter or problem)

This exercise investigates the continuouscompounding formula, using a realistic interestrate. Consider the value of deposited for 3years at interest, compounded n times peryear, for increasing values of n. In this case, theinterest rate per period is and the number ofperiods in 3 years is 3n. So, the value at the end of3 years is given by:a. Complete the following table:A 4000a1 0.05n b3n 4000 c a1 0.05n bnd30.05n ,5%$4000compounding period Effective rateannually 12%quarterlymonthlydailyb. Compare the entries in the second column ofthe table in part a to the number andcomplete the following sentence:As n gets larger and larger, the value ofgets closer and closer to thenumber ? .c. Use your answer to part b to complete thefollowing sentence:As n gets larger and larger, the value ofgets closer and closerto the number ? .d. Compare your answer to part c with the valuegiven by the continuous compounding formula.