Chapter 4 - Exponential Functions - 4.5 The Number e - Exercises and Problems for Section 4.5 - Exercises and Problems - Page 174: 41

We see that the bank with continuously compounded interest has a balance $\$ 14,918.25-14,774.55= \$143.70$ higher.

Find the balances of each investment. The balance in the first bank is $$10,000(1.05)^8=\$ 14,774.55.$$ The balance in the second bank is $$10,000 e^{0.05(8)}=\$ 14,918.25.$$ We see that the bank with continuously compounded interest has a balance $$\$ 14,918.25-14,774.55= \$143.70$$ higher.