Compound Interest
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
 Make sure you know the difference between compound interest and simple interest
 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)
 If p.a. (per annum) is paid compounding monthly, then will be paid each month
 The formula for compound interest allows for this so you do not have to compensate separately
 The interest rate, r, will be per annum (per year)
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
 Where
 Be careful with the k value
 Compounding annually means k = 1
 Compounding halfyearly 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
Exam Tip
 Your GDC will be able to solve some compound interest problems so it is a good idea to make sure you are confident using it, however you must also familiarise yourself with the formula and make sure you can find it in the formula booklet
Worked Example
Kim invests MYR 2000 (Malaysian Ringgit) in an account that pays a nominal annual interest rate of 2.5% compounded monthly. Calculate the amount that Kim will have in her account after 5 years.
Depreciation
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
 Where
 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
Exam Tip
 Although the formula is not the same as the one given in the formula booklet for compound interest, it is very similar
 Practice finding this formula and recognising the differences
Worked Example
Kyle buys a new car for AUD $14 999. The value of the car depreciates by 15% each year.
a)
Find the value of the car after 5 years.
b)
Find the number of years and months it will take for the value of the car to be approximately AUD $9999.