Compounding Interest Monthly, Quarterly, Semi-Annually or Monthly

In our tutorial on long term time value of money, we explained compound interest in the form of annually compounded interest. What happens if the interest is not compounded annually (once a year), but quarterly (4 times a year) or monthly (12 times a year)? In these circumstances, our money would grow much faster at monthly compounding, as opposed to annual compounding. Let's take a look:

C/Y = Compounding Periods Per Year

If investment interest rate is compounded monthly, then C/Y = 12
If investment interest rate is compounded quarterly, then C/Y = 4
If investment interest rate is compounded semi-annually, then C/Y = 2
If investment interest rate is compounded annually, then C/Y = 1

Year	Annual Compounding	Semi-Annual Compounding	Quarterly Compounding	Monthly Compounding
1	$100,000	$100,000	$100,000	$100,000
2	$110,000	$110,250	$110,380	$110,470
3	$121,000	$121,550	$121,640	$121,840
4	$133,100	$134,010	$134,450	$134,820
5	$146,410	$147,750	$148,450	$148,940

Graphical Representation of the above Data

Compounding Interest Effects Long Term Graph

As you can tell from the above graph, the $100,000 that is compounded monthly grows much faster than the $100,000 that is compounded annually. In a matter of 5 years:

$100,000 -> $148,940 (Compounded Monthly)

$100,000 -> $146,419 (Compounded Annually)

Difference = $148,940 - $146,419 = $2521!

Calculations

How did we get all these numbers? Using the time value of money template, we have highlighted the C/Y = 1, C/Y=2, C/Y=4 and C/Y=12 in Blue.

Year 1 Calculations:

1) Annual Compounding:

N=1
I/Y=10%
PV=100
PMT=0
FV=?
P/Y=1
C/Y= 1
Solution: FV = $110

2) Semi-Annual Compounding:

N=1
I/Y=10%
PV=100
PMT=0
FV=?
P/Y=1
C/Y= 2
Solution: FV = $110.25

3) Quarterly Compounding:

N=1
I/Y=10%
PV=100
PMT=0
FV=?
P/Y=1
C/Y= 4
Solution: FV = $110.38

4) Monthly Compounding:

N=1
I/Y=10%
PV=100
PMT=0
FV=?
P/Y=1
C/Y= 12
Solution: FV = $110.47