This is “Simple Interest”, section 6.3 from the book Finance for Managers (v. 0.1).
This book is licensed under a Creative Commons by-nc-sa 3.0 license. See the license for more details, but that basically means you can share this book as long as you credit the author (but see below), don't make money from it, and do make it available to everyone else under the same terms.
This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book.
Normally, the author and publisher would be credited here. However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. Additionally, per the publisher's request, their name has been removed in some passages. More information is available on this project's attribution page.
For more information on the source of this book, or why it is available for free, please see the project's home page. You can browse or download additional books there. You may also download a PDF copy of this book (2 MB) or just this chapter (195 KB), suitable for printing or most e-readers, or a .zip file containing this book's HTML files (for use in a web browser offline).
PLEASE NOTE: This book is currently in draft form; material is not final.
What do you think should happen if Mary wishes to borrow the $9 from Martha for two weeks? Should she assume she’ll only have to pay the same $5 of interest? Of course not! It is likely to expect that Martha will desire more interest to compensate her for the opportunity cost of the second week. So it is always important to note for what period an interest rate applies! For example, it’s no use using a 2-year interest rate if you need a 1-week rate!
Let’s assume that Martha is willing to lend to Mary for the second week for an additional $5; determining interest in each period from outstanding principal only is known as simple interestDetermining interest in each period from outstanding principal only.. Two weeks of borrowing means (2 × $5) = $10 of interest owed, for a final payment of (principal + interest) = ($9 + $10) = $19.
Equation 6.2 Simple Interest for 2 Periodsprincipal + first week’s interest + second week’s interest = FV
The total interest paid is $10 vs. $9 borrowed, so the implied 2-week interest rate is ($10/$9) = 111.11%. Note that this is precisely twice the 1-week rate of 55.56%. To generalize for more periods, since the interest paid will be the same for each period, we can simply multiply the interest rate by the number of periods, n, to get the effective rate for that period.
Equation 6.3 Simple Interest for n PeriodsPV × (1 + nr) = FV