## Understand

In business finance, the time value of money is an idea that worth of a certain amount of money today is more than the same amount in future because of its earning capacity. For example, you have an opportunity to receive $100 today or after six months. Which option will you choose? Based on the idea of the time value of money, you should prefer to receive $100 today because the value of the same amount will decrease in future. After receiving that amount, you can invest it saving account or in your business to gain the profit which would not be possible if you option for the second choice.

## Important Concepts to Understand Time Value of Money

To understand how the value of same amount decrease with the passage of time, following concepts are essentials:

### Simple Interest

It is a fixed amount of money against invested or loan amount. For example, you have invested $100 for two years in a bank with the simple interest rate of 5%. After two years, you will gain $10 from invested amount and your wealth will increase to $110.

### Compound Interest

As compared to simple interest, it is not fixed rather change with respect to remaining principle amount. For example, again you invest $100 in a bank for two years with 5% interest rate. After two years, your wealth will increase as under:

Year 1

Invested amount = $100 and interest income is $5 resulting in increased principle amount of $105

Year 2

Increase invested amount after interest income = $105 and interest income on it will be $5.25 so finally you will be able to get $0.25 more money by compounding interest.

### Present Value

It is simply the reciprocal of compound interest or current worth of money today.

### Future Value

It is the value of the present value of money at a specific time in future.

### Annuity

An annuity is an equal series of cash flows with regular intervals of time, which are calculated using the principle of time value of money. Annuity due, ordinary annuity, and perpetuity are three common types of it.

## Formula

PV = FV (1+r)^{-n}

FV = PV (1+r)^{n}

Where,

PV is present value,

FV is future value,

r is the interest rate, and

n is total no of the period.

## Example

You have $100 today and want to invest in a bank for 5 years with 8% interest rate compounded annually. What would be worth of your money after 5 years?

Solution

FV = $100 (1+0.08)^{5}

FV after 5 years = $146.93

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