Key Concepts

A function is a basic data recipe. It is also an input-output machine. It accepts arguments, and returns the final product of the recipe.

• The function function()
• arguments
• argument values
• argument default values
• explicit vs implicit argument calls
• return values
• arrow vs. equal sign

Loan Calculator

Let’s create a mortgage calculator as a simple example. A mortgage calculator considers the total loan amount (the principal), the interest rate or APR (annual percentage rate), and the period of the loan in order to determine how much needs to be paid each month so that payments are distributed equally across the loan term.

If we look up an amortization (repayment schedule) formula, we see it is calculated as follows:

\[ monthly \ payments = \frac{principal \cdot interest \ rate}{1-(1+interest \ rate)^{- \ loan \ duration}} \]

When we translate this mathematical formula into R code, the new function will look like this:

 calcMortgage <- function( principal, years, APR )
 {
   
    months <- years * 12   # covert years to months
    int.rate <- APR / 12   # convert annual rate to monthly
    
    # amortization formula
    monthly.payment <- ( principal * int.rate ) / 
                       (1 - (1 + int.rate)^(-months) )
    
    monthly.payment <- round( monthly.payment, 2 )
    
    return( monthly.payment )
 
 }

Default Arguments

We can add default values for arguments. These defaults allow us to utilize the function without specifying values for those arguments.

 calcMortgage <- function( principal, years=30, APR=0.05 )
 {
   
    months <- years * 12   # covert years to months
    int.rate <- APR / 12   # convert annual rate to monthly
    
    # amortization formula
    monthly.payment <- ( principal * int.rate ) / 
                       (1 - (1 + int.rate)^(-months) )
    
    monthly.payment <- round( monthly.payment, 2 )
    
    return( monthly.payment )
 
 }

Implicit Argument Calls

An explicit call to arguments always uses the formal argument name such as principal=100000.

You can, however, also use implicit argument calls. These rely on the order arguments are specified in the function, and the order of your values in your call.

Implicit arguments calls can be risky, however, because it is very easy to mix them up.

Object Assignment vs Argument Assignment

principal <- 100000               # never use equals here
calcMortgage( principal=100000 )  # never use arrows here

Your Turn

\[ celsius = ( \ fahrenheit − 32 \ ) × \frac{5}{9} \]

If you want to check your work, 212 degees Fahrenheit is equivalent to 100 degrees Celsius.