Introduction to the time value of money with code

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The first quantitative class for vanilla finance and quantitative finance majors alike has to do with the time value of money. Essentially, it’s a semester-long course driving notions like _$100 today is worth more than $100 a year from today _into the heads of college students and making them work out painful word problems by hand to determine how much they need to invest today to arrive at some value in the future. This is done in tandem with the introduction to perpetuities and annuities as an application to the temporal value differential. Though I wasn’t a fan of working out the computations by hand, I’m a big fan of coding them in Python for ease of use.

Time Value of Money

Risk-free interest rates — in practice proxied by U.S. treasury bills, notes, and bonds are responsible for the difference in the value of money over time. Higher-level courses covering subjects including derivatives and securities pricing always take into account the time value of money in their pricing formulae, making this topic what algebra is to calculus.

Consider the current risk-free rate is 8% per annum. To receive $100 today means an immediate investment can be made at the risk-free rate…

After a year $100 at the risk-free rate is $108. Therefore receiving $100 today would be worth more than receiving $100 one year from today all else equal.

In the previous example, compounding (reinvesting periodic interest payments throughout the year) was completely disregarded. Let’s look at another example where we take into account a compounding effect.

Consider the current risk-free rate is 8% per annum, and the compounding frequency is once per month. To receive $100 today means an immediate investment with monthly compounding can be made at the risk-free rate…

#economics #python #business #finance #investing