This is a nice article, but it ignores the difference between nominal and effective interest rates. Simple division only works on nominal interest rates, but you are more likely to encounter effective rates which need to be converted first.
> If I have €1000 in an investment that grows with 5% annually and I contribute €100 per month for the next 10 years, how much will accrue? … This can be calculated with the following formula: … FV(5% ÷ 12, 10 × 12, 100, 1000) = -17,175.24
If your investment grows 5% annually then this is the effective rate, not the nominal rate. The monthly interest rate is thus not 5%÷12 but rather ((1+5%)^(1÷12))-1, due to compounding—this can also be written NOMINAL(rate, nper)÷nper. You can see the difference if you compare results with different numbers of periods but no contributions—the result should be the same no matter how the time is divided up.
# Basic formula, 5% annual growth for 10 years with 1-year period
FV(5%, 10, 0, -1000, 0) ⇒ $1,628.89
# As per article, 5% annually for 10 years but with monthly periods
FV(5%/12, 10*12, 0, -1000, 0) ⇒ $1,647.01
# Converting to the nominal rate before division gives consistent results
FV(NOMINAL(5%, 12)/12, 10*12, 0, -1000, 0) ⇒ $1,628.89
> If I have €1000 in an investment that grows with 5% annually and I contribute €100 per month for the next 10 years, how much will accrue? … This can be calculated with the following formula: … FV(5% ÷ 12, 10 × 12, 100, 1000) = -17,175.24
If your investment grows 5% annually then this is the effective rate, not the nominal rate. The monthly interest rate is thus not 5%÷12 but rather ((1+5%)^(1÷12))-1, due to compounding—this can also be written NOMINAL(rate, nper)÷nper. You can see the difference if you compare results with different numbers of periods but no contributions—the result should be the same no matter how the time is divided up.