2Basics of Finance
2.1 Introduction
The value of money over time is a very important concept in financial mathematics. A dollar that is earned today is valued higher than a dollar that will be earned in a year's time. This is because a dollar earned today can be invested today and accrue interest, making this dollar worth more in a year. We can then calculate how much money we will need to invest now to have 
dollars in a certain time frame. For example, if we invest $100 at 5% interest for a year, we will have 100(5%) + 100 = $105 at the end of the year. A question that often arises is how can one model interest mathematically? This can be modeled by an amount 
in the bank at time 
. The amount of interest gained during an elapsed time of 
is represented as 
. Since interest is proportional to the amount of money in the account, given the interest rate 
and time step , we can then write ...
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