IB DP Maths: AI HL复习笔记1.4.1 Compound Interest & Depreciation

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