Continuous compounding: This is a continuation . In this exercise we examine the relationship between the APR and the APY when interest is compounded continuously—in other words, at every instant. We...

Continuous compounding: This is a continuation . In this exercise we examine the relationship between the APR and the APY when interest is compounded continuously—in other words, at every instant. We will see by means of an example that the relationship is

if both the APR and the APY are in decimal form and interest is compounded continuously. Assume that the APR is 10%, or 0.1 as a decimal.

a. The yearly growth factor for continuous compounding is just the limiting value of the function given by the formula in part b . Find that limiting value to four decimal places.

b. Compute eAPR with anAPR of 0.1 (as a decimal).

c. Use your answers to parts a and b to verify that Equation (4.1) holds in the case where the APR is 10%. Note: On the basis of part a, one conclusion is that there is a limit to the increase in the yearly growth factor (and hence in the APY) as the number of compounding periods increases. We might have expected the APY to increase without limit for more and more frequent compounding.