Compounding Interest Monthly, Quarterly,
Semi-Annually or Monthly
More Time Value of Money Tutorials
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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
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
