Basics of Interest Rates

This is a note on the basics of interest rates. There are two ideas to keep in mind, the rate and how often interest is compounded. The rate is usually given as an annual figure, e.g. 7.5% annual annual percentage rate. However, that interest can be compounded, annually, quarterly, monthly, weekly, daily, even continuously! Let r the the annual interest rate and let B be the balance in your bank account:

• compounded annually means that once a year a new balance is computed according to the rule:
Bnew = Bold + Bold* r / 100
• compounded quarterly means that once every three months a new balance is computed according to the rule:
Bnew = Bold + Bold* (r / 4) / 100
i.e. interest is computed 4 times a year, but at one fourth of the "annual" rate.

• compounded monthly means that every month a new balance is computed according to the rule:
Bnew = Bold + Bold* (r / 12) / 100
i.e. interest is computed 12 times a year, but at 1/12th of the "annual" rate.

Christopher W Brown
Last modified: Mon Sep 13 16:57:16 EDT 2004