Description

CompoundInterestλ() is one of the hard-to-remember-formula functions. Function names are easier to remember than formulas. This function calculates accumulated principal plus compounded interest based on APR, compounding frequency per year, and months invested or borrowed. CompoundInterestλ uses this formula:

=Principal * ( 1 + (AnnualRate / PeriodsPerYear)) ^ (PeriodsPerYear * Years)

This is essentially a 'transparent' and simplified version of Excel's FV() function. Both are shown in the example below.

Transparent:

FV()'s inner workings are not visible to us and if they were visible, their C# code would not be understandable to almost any of us. 5g functions' inner workings are visible in Name Manager or, better still, Microsoft's free add-in: Advanced Formula Environment and their formulas are 100% native Excel which should be familiar to all modelers. 

Simplified:

FV() requires us to adjust the rate and number of periods to accommodate monthly or quarterly compounding intervals. FV is also more flexible in that it can include payments but when payments are not part of the solution, payments only ad complexity.

Benefit:
Packaging difficult to remember formulas into functions prevents errors due to remembering incorrectly or mistyping the formula. Functions also prompt for inputs with human readable language so its less likely we will use the wrong assumptions.

Example

Below we are borrowing 10,000 at an APR of 8%. We want to know how much principle plus interest we will owe given different compounding intervals and months held.

At the bottom, we enter our function, CompoundInterestλ(), and provide its inputs: Principle, Annual Rate, Compounding Periods Per Year, and Months. As we make changes to Compounding Periods Per Year and Years, our function projects the principal plus interest. 

At the top is a compounding corkscrew that we can use to test CompoundInterestλ(). The function is calculating correctly when values highlighted in light copper match, which they do. At the bottom we also see FV()'s formula and results which also confirm CompoundInterestλ() is doing what is intended.