Time value of money

Time Value of Money (TVM) is one of the most important concept that I have learn at the start of my investment journey. TVM is based on the concept that a dollar you have today will be worth more than a dollar you get in the future. The money that you hold today is worth more than future value because you have a chance to invest that money or earn interest now.

Applying more to that concept, for example it is a better choice to receive a lump sum of $400 than to receive $100 in 4 different payouts. However the opposite analogy should apply for payment. Preferably it is better to defer payment as long as possible than to pay a lump sum amount now.

While investing, many times you will encounter the need to calculate that illusionary future figure of the amount you invested now. For example, if you are to invest a lump sum of $1000 at an interest rate of 6% annually, what is the investment amount after 5 years assuming the interest is compounded annually? Before I show the calculation for this example, let me just explain the definition of Future Value (FV) and Present Value (PV) first.

FV is the amount of money that an investment (the PV) made today will grow at a future date. Since money has time value, FV is greater than PV.

PV is an amount today that is equivalent to a future amount (the FV) discounted by an interest rate. Since money has time value, PV is less than the FV.

The relationship between FV and PV can be expressed as:
FV = PV (1 + i)^n
where i = interest rate per period
n = number of compounding periods

So back to the example that I quoted above, you can calculate the FV to be:
FV = $1000 (1 + 0.06)^ 5 = $1338.23

Now let us see what happens when the interest is compounded monthly. Since the annual interest rate is 6%, therefore its monthly interest rate or interest rate per period will be 0.5%. The number of compounding periods will be 60 in this case.
FV = $1000 (1 + 0.005)^60 = $1348.85

You can see the difference in FV for an investment that is compounded monthly and yearly. Therefore when looking into loans or investments, one of the important factor to consider before making a decision is the type of interest rate. I hope from the examples above you can have a better understanding of TVM.