Chapter 4 – (3 marks) The Principles Of The Time Value Of Money Flashcards
This chapter is only 3 marks so DONT SPEND TOO MUCH TIME ON IT
Being heavily calculation-based, this chapter tends to suck people in, and many candidates spend time struggling to understand the formulae to the detriment of other chapters.
Do not let this happen to you!
This is the chapter (if any) that needs a compounding calculator. We will show you both the way to use this and, as these can vary, a way to do compounding calculations on a standard calculator as well.
several calculations over the coming pages, all of which are important for you to know but, as mentioned in the chapter introduction, there are only 3 marks available from this chapter. You should not allow this to take over your revision.
To calculate returns and values, there are a few definitions to learn:
Present Value (PV)
Time Period (n)
Interest Rate (r)
Future Value (FV)
Present Value (PV) = amount invested today
Time Period (n) = The number of times that interest is paid. If its a 5 year investment where interest is paid annually n = 5 but if its a 5 year investment where interest is paid monthly
n = 60
Interest Rate (r) = the value of each interest payment that is made. This also changes depending on when the interest is paid. R also must be in its decimal form
Future Value (FV)
What is compound interest
What is the formula to calculate compound interest?
Compound interest is interest earned on interest
FV = PV(1+r)^n
The formula to calculate compound interest is FV = PV(1+r)^n
What would a sum of £3000 invested at an interest rate of 4% for 5 years increase to?
The formula to calculate compound interest is FV = PV(1+r)^n
Occasionally you will get a question that provides you with a gross interest rate and asks you for a net return. These need adjusting for tax
Using the example above, you would reduce the gross interest rate by the tax rate paid so if Jennifer had been a higher rate taxpayer you would have reduced the 6% by 40%; i.e. 3.6%, and an additional rate taxpayer by 45%; i.e. 3.3%
The formula to calculate compound interest is FV = PV(1+r)^n
Many accounts pay interest more regularly than annually, for example monthly. Tell me how questions where interest is earned monthly is calculated
Question:
£7000 is invested into a savings account. Interest is paid monthly at an annual rate of 6%. How much will this be at the end of the year?
The formula to calculate compound interest is FV = PV(1+r)^n
R is the value of an interest payment. Because it has an annual rate of 6% and it is paid monthly R = 6%/12 = 0.5%
Be careful because you must decimilise 0.5% which is 0.005
There are 12 interest payments because the interest is paid monthly and he would like to know the value in a years time so
n = 12
Therefore
7000(1+0.005)^12 = £7431.74
The formula to calculate compound interest is FV = PV(1+r)^n
See image for an example of how to calculate quarterly interest
r = the value of each interest payment that is made
n = is the number of interest is paid
So for both the above keep an eye on whether the question is asking for monthly, annual, quarterly interest etc because both these will change depending on how the interest is paid
You must also convert r into its decimal form
Sometimes you may be required to calculate other info such as annual percentage rate where you are given the present value and the future value. This obvs means you will need to rearrange the formula: FV = PV(1+r)^n
There is a time value of money. ie, The same interest rate, if re-invested, is greater if paid more frequently (see image)
Because of this fact it can be difficult to compare which provider is offering the best rate for loans or savings because providers vary in when they pay interest, the rate they offer, and the length of terms. However, there is a formula in order to do this.
What is the formula?
The ‘effective annual rate’ formula
Effective annual rate is also known as annual percentage rate (APR) or annual equivalent rate (AER).
It is the nominal rate compounded and is the best comparison of rates offered by banks and building societies for both saving and loans.
EAR = (1 + r/n)^n - 1
SEE EXAMPLE
The ‘effective annual rate’ formula is used
EAR = (1 + r/n)^n - 1
What is effective annual rate also known as?
Annual percentage rate (APR)
or
Annual equivalent rate (AER).
What is Annual equivalent rate (AER) also known as?
effective annual rate (EAR)
or
Annual percentage rate (APR)
Formula is:
EAR = (1 + r/n)^n - 1
Question
What is the difference between ‘real returns’ and ‘nominal returns’?
Nominal returns ignore inflation.
Real returns take inflation into account. Real return = nominal return minus inflation.
Nominal returns ignore inflation.
‘Real returns’ take inflation into account. It is the nominal return minus inflation.
This is an exam style question of this
real value = real return in relation to this question
