These concepts tell you how much your money will grow if deposited in a bank (future value), how much promised future payments are worth today (present value), and what percentage rate of return you’re getting on your investments (internal rate of return).
Future value (FV) tells you the value in the future of money deposited in a bank account today and left in the account to draw interest. The future value $X deposited today in an account paying r% interest annually and left in the account for n years is X*(1+r) . Future value is our first illustration of compound interest—it incorporates the principle that you earn interest on interest. If this sounds confusing, read on.
Suppose you put $100 in a savings account in your bank today and that the bank pays you 6% interest at the end of every year. If you leave the money in the bank for one year, you will have $106 after one year: $100 of the original savings balance + $6 in interest.
In this book we will often match our mathematical notation to that used by Excel. Since in Excel multiplication is indicated by a star “*”, we will generally write 6%*$106 = $6.36, even
though this is not necessary. Similarly we will sometimes write (1.10)3 as 1.10^3. In order to confuse you, we make no promises about consistency!
We use the words “Year 0,” “Today,” and “Beginning of year 1” as synonyms. This often causes confusion in finance. For example, “$100 at the beginning of year 2” is the same as “$100 at the end of year 1.” Note that we often use “in year 1” to mean “end of year 1”: For example: “An investment costs $300 today and pays off $600 in year 1.”
There’s a lot of confusion on this subject in finance courses and texts. If you’re at loss to understand what someone means, ask for a drawing; better yet, ask for an Excel spreadsheet.
