Compound Growth

Compound Growth: Interest §

• Interest is at the root of making money work for you. It is the price paid for the use of money
  • For example when you borrow money, you pay it back plus interest. i.e. borrowing from a bank to buy a car
  • When you are borrowing money you want to find the lowest interest rate you can get
  • When investing money or depositing to an interest-bearing account, you want a higher interest rate
• Investment gains earned in the first time period are put to work in the second time period to earn more investment returns
  • The key here is time
  • Interest is exponential (even if not REALLY exponential like rabbit populations) so starting small can still grow to very big
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• When you deposit money into a savings account at a bank or credit union, you are really LENDING it to the financial institution
  • The bank pays you back interest for the use of your money
  • You make a low risk loan because you can get your money back at any time
  • Your savings deposit is protected against loss
  • The Federal Deposit Insurance Corporation (FDIC) and the National Credit Union Administration (NCUA) protect your deposit up to $250,000
• Two different interest rate formulas (commonly)
• APR - Annual Percentage Rate
  • This is used when the compounding period of interest is deposited to your account more than once a year
  • The APR becomes the annual sum of the periodic interest rates applied to the account without considering the effect of compound growth
  • $\text{APR}=\text{Periodic Interest Rate}\times \text{Number of Periods in the Year}$
  • If you are a saver the amount of interest you get will be higher than the APR percentage because each interest payment is applied to the compounding balance
  • This works in reverse for borrowers though, so many credit card interest rates are quoted as an APR
• APY - Annual Percentage Yield
  • This is the actual rate of interest you will earn on a starting balance and takes into consideration the compound growth or additional interest that your interest earns
  • The APY will always be higher than the APR when there are more than one compounding periods per year so commonly banks will quote rates in APR for loans and APY for savings
  • $\text{APY}=[(1+\text{Periodic Interest Rate}{)}^{\text{Number of Periods in year}}]-1$
• EXAMPLE
  • Say the bank pays you 0.2% monthly interest on your savings
  • APR would be $0.2\%\text{ per month }\times 12\text{ months }=2.4\%\text{ per year}$
  • APY would be $[(1+0.002{)}^{12}]-1=0.0243$ or 2.43%
• Strategically using interest
  • Minimize interest payments
    • The only way to stop interest is eliminate the cause - the loan principal amount accruing interest
    • Pay off credit card debt in full
    • Wait to spend money: this will often determine whether you pay interest or receive interest
  • The advantages of patient planning
    • Some financial accounts have early withdrawal penalties
    • Other financial products, like U.S. savings bonds, will not let you cash in the bond for at least 1 year