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Present and future value
It is common practice to use the terminology Present Value, or PV, for the sum of money involved at the start of a loan or investment and Future Value, or FV, for the final balance.
In other words, FV is what results after interest has acted on PV.
This jargon applies equally to investments or loans:
- In the case of an investment the amount of money that is deposited or invested is the PV and the final balance is the FV
- In the case of a loan the sum borrowed is the PV and the amount finally paid back is the FV
Other terms, such as principal, are used for PV but for the remainder of this book PV and FV will be used to denote the value before and after the action of interest respectively.
Notice that the relationship between PV and FV depends on the type of situation we are considering.
For example, in the case of simple interest of I% over n interest bearing periods the FV is given by:
You should be able to recognise this as just increasing the PV by I*n%.
Comparing simple interest
In the situation where interest is paid on a PV that does not change over time then it is very easy to compare different interest rates.
For example, if a deposit pays 2% interest per month then over a 12 month period the total amount paid in interest is simply:
This implies that to receive 2% per month is equivalent to receiving 24% per annum.
This same reasoning applies to any interest rate over any time period.
- All we have to do to compare the rates is to convert them to the equivalent rate per annum
For example, 10% paid every six months, i.e. two interest bearing periods per annum, is equivalent to a rate of 0.10*2 i.e. 20% per annum.
In other words, for simple interest rates converting between different periods really is just a matter of multiplying by the ratio of the periods.
- 0.5%, i.e. half a percent, paid daily is equivalent to 0.5*365% or 185% per annum
- 1% paid bi-monthly is the same as 0.5% paid monthly
- a 50% return over 10 years is equivalent to 5% per annum
and so on.
Notice that for all of these examples to be correct the situation must correspond to `simple interest’, i.e. the interest calculated is not added to the PV.
The value of money
Simple though this conversion to an annual rate is, it misses some important points.
In particular, when interest is paid is also an important consideration in determining what it is worth. Payments made now are generally considered to be worth more than equal payments made in the future. This means that 12 monthly payments are worth more than the same total payment made at the end of the 12-month period.
To understand the why and how of this situation we will have to look more carefully at the way time affects the value of money.
There is also the question of what happens if the interest does effect the value of the principal. For example, you may choose to add the interest to the deposit or to increase the debt by deferring interest payments. This leads us on to consider compound interest.