Introduction to time value of money

Let's use a very simple example to illustrate. Assume that $100 is deposited in a bank today with an annual interest rate of 10%. What is the value of the deposit one year later? Here is the timeline with the dates and cash flows:

Obviously, our annual interest payment will be $10, that is, 100*0.1=10. Thus, the total value will be 110, that is, 100 + 10. The original $100 is principal. Alternatively, we have the following result:

Assume that $100 will be kept in the bank for two years with the same 10% annual interest rate for two years. What will be the future value at the end of year two?

Since at the end of the first year, we have $110 and by applying the same logic, the future value at the end of year two should be:

Since 110 = 100*(1+0.1), then we have the following expression:

If $100 is deposited for five years with an annual interest rate of 10%, what is the future value at the end of year five? Based on the preceding logic, we could have the...