Fundamentals of Financial Mathematics and the Time Value of Money

Financial mathematics is defined as the study of how money grows or declines over time.
The central and most fundamental concept in this study is the Time Value of Money (TVM).
The Time Value of Money (TVM) principle states that money today is worth more than the same amount in the future because of its earning potential.

There are four distinct reasons why money in the present is valued higher than money in the future:

Investment opportunities (earning interest): Money available now can be put into investments to generate additional income or interest.
Inflation: This economic factor reduces purchasing power over time, meaning a set amount of money will buy less in the future than it does today.
Risk/uncertainty: Future payments carry the risk that they may not be received, whereas money held today is certain.
Preference for current consumption: There is an inherent preference to use and consume resources in the present rather than waiting for a future date.

The introduction of interest is fundamental to the study of finance.
Interest is defined as the fee paid for the use of money over time. It can also be viewed as the fee earned for providing the use of money.
Borrowing and lending are essentially opposite sides of the same transaction, similar to how getting financing and investing are related perspectives of a single financial exchange.

The calculation of interest fees is dependent on three primary variables:
- The Principal: This is the amount borrowed or invested.
- The Annual Rate of Interest: This is the specific rate charged for the use of the funds on a yearly basis.
- The Length of Time: This is the duration for which the money is borrowed or utilized.
Bank Discount: This is a specific type of fee sometimes referred to as "interest in advance." It represents a fee paid for the use of money overtime, comparable to standard interest charges.