83 K1.01: Simple and Compound Interest

Finance: Simple and Compound Interest

Questions Explored:

• What is the difference between simple and compound interest?
• I want to deposit a lump sum of money into an account earning interest and leave it there. What will I have in the future?
• What lump sum should I deposit into an account earning interest in order to have a certain future value?
• What happens to my credit card balance if I don’t pay any of it for a period of time?

Terms:

• Principal – initial amount of the investment or loan
• Interest – amount paid to you by the lender for investing with them, or, the fee you pay for borrowing money
• Simple interest – interest paid only on the original principal
• Compound interest – interest paid on both the original principal and any interest that has been added to the original principal
• Annual percentage rate (APR) – % of interest earned or owed each year; may need to be divided up for smaller time periods (i.e. monthly, quarterly, etc.), APR does not take compounding into account
• Compounding period – period at the end of which interest is computed
  • o Annually = once a year
  • o Semiannually = twice a year
  • o Quarterly = four times a year
  • o Monthly = twelve times a year
  • o Daily = 365 times a year (was 360 in the past before computers were readily available to make math easier for the banker)
• Savings accounts – accounts into which you deposit money
  • o Currently savings accounts have a very low interest rate
  • o Standard savings accounts, money market accounts, and CDs (certificate of deposit) are a few different types of savings accounts with different interest rates and withdrawal restrictions.
• FDIC – (Federal Deposit Insurance Corporation) guarantees safety of bank deposits currently up to $250,000 per depositor per bank (as of 2016)
• Bonds – when you purchase a bond, the bond issuer is in debt to the bond holder and pays the bond holder interest on the bond and/or repays the principal later to the holder
  • o The bond holder is the lender and has loaned the bond issuer money, who is now the debtor.
  • o There are many types of bonds: Treasury bonds, corporate bonds, municipal bonds, etc.
  • o Bonds may have a fixed or variable interest rate.
  • o Interest may be simple or compound.
  • o Bonds may or may not be inflation-linked.
  • o Bonds may or may not have tax advantages
  • o Bonds may be low or high risk
• Credit card – system of payment that allows someone to purchase goods or services with the promise that the money will be repaid
• Annual percentage yield (APY or effective annual yield or effective yield or yield) – actual percentage by which a balance increases in one year, slightly different than the APR since it takes compounding into account

Rules

Simple interest:  The amount of interest earned is the same percentage of the original principal every year.

Compound interest:  The amount of interest earned in each time period is computed on the accumulated amount of money in the account at the beginning of that time period.

Annual Percentage Yield: The annual percentage yield of an investment is computed by finding the relative change from the initial balance to the balance at the end of the same year.