## Time Value of Money

One of the main concepts of Finance is an understanding of time value of money. It is an idea that money available at the present time is worth more than the same amount in the future due to its potential to increase. Finance teaches us that money can earn interest, so then any amount of money is worth more today then in 5 years.

For example: The sooner money can be deposited in a saving or Cd account the sooner the money can start to earn interest. If we can find 5% interest rate, using $100 being invested today, in one year, your $100 will be worth $105. Inversely $100 received one year from now is only worth $95.24 today.

FV = Future Value

PV = Present Value

i = The present interest per period

n = The number of compounding periods

If you were to put $100 in the bank and you were somehow to find 10% interest per year for 2 years then

What is the future value of $50 in 5 years if the interest rate is 5%? i = 0.05

For this situation, we will use the formula above.

FV = $50 * (1+0.05) ^ 5

FV = $50 * (1.276282)

FV = $63.81

So here we can see that after 5 years at 5% we had an increase of $13.81. The sooner we can start putting money away, the power and influence interest can have on the principle investment.

Again, we will use the same formula as above with one exception. we will compound this twice in one year.

FV = $50 * (1+(0.05/2)) ^ (5*2)

FV = $50 * (1.280085)

FV = $64.00

It is important to remember that when there is compounding more than once, we need to divide interest rates by number of payouts per year and also multiply the number of payouts per year.

Again, we will use the same formula as above with one exception. we will compound this twelve times in one year.

FV = $50 * (1+(0.05/12)) ^ (5*12)

FV = $50 * (1.283359)

FV = $43.63

There is a function in excel that makes this incredibility easy for us understand the time value of money. It is called the Future vale (FV) function. When you type =fv, what you are asking excel to do is to find out what the future value is. By doing some homework, knowing what the interest rate is and knowing how long your going to keep it in that account will be of great benefit for you.

So lets use the last example. We are keeping this money in this particular account with these assumptions

For example: The sooner money can be deposited in a saving or Cd account the sooner the money can start to earn interest. If we can find 5% interest rate, using $100 being invested today, in one year, your $100 will be worth $105. Inversely $100 received one year from now is only worth $95.24 today.

**FV = PV (1 + I) ^N**FV = Future Value

PV = Present Value

i = The present interest per period

n = The number of compounding periods

If you were to put $100 in the bank and you were somehow to find 10% interest per year for 2 years then

- The Future Value will be $121.00
- Remember that the Present Value was $100

**Future Value Compounded Annually**What is the future value of $50 in 5 years if the interest rate is 5%? i = 0.05

For this situation, we will use the formula above.

FV = $50 * (1+0.05) ^ 5

FV = $50 * (1.276282)

FV = $63.81

So here we can see that after 5 years at 5% we had an increase of $13.81. The sooner we can start putting money away, the power and influence interest can have on the principle investment.

**Future Value Compounded Semi-Annually**Again, we will use the same formula as above with one exception. we will compound this twice in one year.

FV = $50 * (1+(0.05/2)) ^ (5*2)

FV = $50 * (1.280085)

FV = $64.00

It is important to remember that when there is compounding more than once, we need to divide interest rates by number of payouts per year and also multiply the number of payouts per year.

**Future Value Compounded Monthly**Again, we will use the same formula as above with one exception. we will compound this twelve times in one year.

FV = $50 * (1+(0.05/12)) ^ (5*12)

FV = $50 * (1.283359)

FV = $43.63

There is a function in excel that makes this incredibility easy for us understand the time value of money. It is called the Future vale (FV) function. When you type =fv, what you are asking excel to do is to find out what the future value is. By doing some homework, knowing what the interest rate is and knowing how long your going to keep it in that account will be of great benefit for you.

So lets use the last example. We are keeping this money in this particular account with these assumptions

- we have $50 today
- we are able to find 5% interest rate
- this particular account will be compounded monthly