Question 1. Sometimes the limit of a certain function is quite unintuitive. In this worksheet, we will investigate one of the most important limits in mathematics and its ap- plications. In 1683, Jacob Bernoulli studied the following question about compounding in- terest: An account starts with $1,000, and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value of the account will be $2,000. What happens if the interest is computed and credited more frequently during the year? For instance, if the interest is credited twice in the year, the interest rate for each 6 months will be 50 %. So after 6 months, the initial $1,000 is multiplied by 1+0.5 = 1.5 and we have 1000 x 1.5 = $1,500. At the end of the year (after another 6 months), the interest must be calculated again by multiplying 1.5, so it yields $1500 x 1.5 = $2,250 at the end of the year. Note that we are multiplying 1.5 twice, so we can describe the value as 1000 x 1.52. This ratio limc+0+ f(x) f(0) of the limit, and the initial value f(0) is called Euler's number e. It is one of the most intriguing, important and mysterious numbers, because it appears many different context which are seemingly unrelated to each others. Your calculator surely has a button for e.2 (i) When the nominal interest rate is 100 % , what is the possible upper bound of the APY? Can you describe it by using Euler's constant e? *I found the APY but need help with descrining it by using Euler's constante $2.718.2818 - 1000 = 1.718 = APY 1000