# Time value of money

A separate article treats the time value of an option.

The time value of money (TVM) or the present discounted value is one of the basic concepts of finance. We know that if we deposit money in a bank account we will receive interest. Because of this, we prefer to receive money today rather than the same amount in the future. Money we receive today is more valuable to us than money received in the future by the amount of interest we can earn with the money. This is referred to as the time value or cash value of money. It is the change in purchasing power of money over time.

It also takes into account default risk and inflation. 100 monetary units today is a sure thing and can be enjoyed now. In 5 years that money could be worthless or not returned to the investor.

To adjust for this time value, we use two simple formulae. The present value formula is used to discount future money streams: that is, to convert future amounts to their equivalent present day amounts. The future value formula is used to convert today's money into the equivalent amount at some time in the future (i.e., to compound money...either a lump sum or streams of payments).

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## Future value

One hundred units invested today at a 5% per year interest rate will yield:

[itex]{\rm Future\ value} ={\rm present\ amount}\times(1+{\rm interest\ rate})^{\rm term}=\ 100\times{(1+0.05)^1}=\ 105[itex]

after 1 year. So, the future value of 100 units in 1 year at 5% per year is 105 units. See future value for details.

There is a separate formula to calculate Future Value of annuities:

[itex]{\rm Future\ value\ of\ annuities} = \frac{((1 + {\rm interest\ rate})^{\rm term}) - 1)}{\rm interest\ rate} \times {\rm present\ amount}[itex]

## Present value

One hundred units 1 year from now at 5% interest rate is today worth:

[itex]{\rm Present\ value}=\frac{\rm future\ amount}{(1+{\rm interest\ rate})^{\rm term}}=\frac{\ 100}{1.05}=\ 95.23[itex]

So the present value of 100 units 1 year from now at 5% is 95.23 units. See present value for details.

There is a separate formula to calculate the present value of annuities:

[itex]{\rm Present\ value\ of\ annuity}=\frac{1 - (1 + {\rm interest\ rate})^{(-{\rm term})}}{\rm interest\ rate}*{\rm future\ amount}[itex]

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