What is compound interest?

• Interest is a small percentage paid by a bank or company that is added on to an initial investment
  • Interest can also refer to an amount paid on a loan or debt, however IB compound interest questions will always refer to interest on?investments
• Compound interest?is where interest is paid on?both the initial investment?and any interest that has?already been paid
  • Make sure you know the difference between compound interest and simple interest
    • Simple interest pays interest only on the initial investment
• The interest paid each time will increase as it is a percentage of a higher number
• Compound interest will be paid in instalments in a given timeframe
  • The interest rate,?r, will be per annum (per year)
    • This could be written?r %?p.a.
  • Look out for phrases such as?compounding annually?(interest paid yearly)?or compounding monthly?(interest paid monthly)
    • The formula for compound interest allows for this so you do not have to compensate separately

How is compound interest calculated?

• The formula for calculating compound interest is:
  • Where
    • FV?is the future value
    • PV?is the present value
    • n?is the number of years
    • k?is the number of compounding periods per year
    • r %?is the nominal annual rate of interest
  • This formula is?given in the formula booklet, you do not have to remember it
• Be careful with the?k?value
  • Compounding annually means?k?= 1
  • Compounding half-yearly means?k?= 2
  • Compounding quarterly means?k?= 4
  • Compounding monthly means?k?= 12
• Your GDC will have a finance solver app on it which you can use to find the future value
  • This may also be called the TVM (time value of money) solver
  • You will have to enter the information from the question into your calculator
• Be aware that many questions will be set up such that you will have to use the formula
  • So for compound interest questions it is better to use the formula from your formula booklet than your GDC

What is depreciation?

• Depreciation is when something looses value over time
  • The most common examples of depreciation are the value of cars and technology or the temperature of a cooling cup of coffee

How is compound depreciation calculated?

• The formula for calculating compound depreciation is:
  • Where
    • FV?is the future value
    • PV?is the present value
    • n?is the number of years
    • r%?is the rate of depreciation
  • This formula is?not?given in the formula booklet, however it is almost the same as the formula for compound interest but
    • with a?subtraction?instead of an addition
    • the value of?k?will always be 1
• Your GDC?could?again be used to solve some compound depreciation questions, but watch out for those which are set up such that you will have to use the formula