# Time Value of Money

The Time Value of Money (TVM) is a very important concept that tells us the following:

A pound received today is worth more than a pound received in the future.

A pound received in the future is worth less than a pound received today.

The cost of money for a period of time is its time value and is measured by an interest rate for that period.

### Question

Lets assume someone said to you, give me a £50 and I will give you £50 back in 2 years time.

Is this a good investment ?

The answer is obviously No, because you could invest this money for 2 years and earn interest.

### Question

Lets assume you buy a product for £50 today and have 2 months to pay for it.

When should you pay ?

The answer is at the end of the 2 months, because you could invest this money for 2 months and earn interest.

### Opportunity Cost of Money

If you deposit £50 at the bank for a year with a fixed interest rate of 10% a year with no risk, then 10% is your opportunity cost of money.

It only makes sense to put your money somewhere else if you think you can earn more than 10% a year.

### Effective or Nominal

A interest rate can be quoted as Effective Rate or Nominal Rate.

If you want to compare interest rates you need to make sure that the compounding frequencies are the same.

If you want to compare nominal interest rates that have different compounding frequencies you can convert them to their effective interest rates.

An effective interest rate is an interest rate that is compounded every year.

A nominal interest rate is an interest rate that is compounded over a period of less than 1 year.

### Important

Interest rates used in the Financial-Markets are generally quoted as nominal interest rates per annum even if the borrowing or lending period is shorter than a year.

When you are converting semi-annual to annual (or the other way) the financial market convention is just to multiply by (or divide by) 2.

In the context of bonds, coupon rates are examples of nominal interest rates.

When interest is compounded annually the nominal interest rate equals the effective interest rate.

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