|
The Big Picture. . . Compounding for Mathematicians
If you are a mathematician at heart, and you want to know the ins and outs of compounding, here it is. This section includes the formulas and examples.
How to know if your plan is on track, and doing the math for your annuity.
|
|
How Compounding Works Magic
Interest (I) is determined by the amount we have saved or invested principal (p) ,
the rate (r) we earn, and the length of time (t) we
can leave the amount invested, as expressed by the following equation:
I = p x r x t
Compounding means that every so often we calculate the interest,
add it to the principal, and use the higher principal for
the next calculation of interest to arrive at a future value.
To get from the original principal-or present value-to
the future value, we use the following equation (where i is
the interest rate per period and n
is the number of compounding periods):
FV = PV (1+i)n
What does all this mean? It means that the future value of
your investment depends on what you set aside today (present
value), what rate you earn (i),
and the number of times the rate is compounded (n).
Doing the Math for an Annuity
A series of equal periodic payments is called an annuity.
To get from the future value of the annuity (FVA) to the periodic
payment (PMT), we use the following equation (where i
is the interest rate per period and n
is the number of periods):
PMT= FVA x 1 % [n-1]
This means that the periodic payment or annuity investment you must make depends
on the future value (or amount of your goal), what rate you earn i,
and the number of payments you make n. Therefore, to keep
your payments (delayed consumption) to a minimum, you should:
- seek the highest
rate available for the amount of risk you can tolerate make a habit of regular
savings and investments
- hold your investments for the long term
Find
out when your savings plan will make you a millionaire!
| 
