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#### Ronald R. Dodge, Jr.

following formula when it's way too simplistic using the simple interest

rate rule that has no practical use in life given how money works or even

how anything else works in life:

(FV-PV)/PV/NP

FV = Redemption Amount

PV = Initial Investment Amount

NP = Number of Years (Normally thought of as number of periods during the

time period, which in this case, 1 year is one period for how the formula is

setup)

To come up with the actual interest rate using the compounding interest

method, one must use the following formula:

(FV/PV)^(1/NP)-1

Under the simple interest method the INTRATE formula uses, for cost of

living that is assumed to double every 10 years, it returns 10%

Obviously, things don't go up by 10% every year, which would mean after 10

years, things would cost 159.3742% more than what they had cost at first as

a result of PV*(1.1^10-1)

To use the formula that I have stated, MS has no financial function to use

that particular formula (at least not built into the Analysis Tookpak

Add-in).

FV/PV = 2

NP = 10

2^1/10-1 = 2^0.10-1=0.071773463

Hence the real annual effective rate for the cost of living to double every

10 years is 7.1773463%, which most people just round to 7.2%, which then has

led to the rule of 72 that says to divide 72 by the interest rate and divide

by 100.

Example:

Interest rate is 8.00%

In the computer form, it would show up as 72/.08/100

which then would say it would take 9 years to double.

Of course, rule of 72 isn't a perfect thing as it's only an estimate and

only works within a certain range. If one really want to know how many

years it would take for such investment to double at a such stated APR, then

they would need to use the following formula:

(LOG(FV)-LOG(PV))/LOG(1+R)=NP

Example

Find out how long it would take for an investment to double such as going

from 1 to 2 with a stated APR compounded only one time per year

(LOG(2)-LOG(1))/(LOG(1.08)=9.006468 years

I also have noticed Excel doesn't have this formula in it either.

--

Thanks,

Ronald R. Dodge, Jr.

Production Statistician

Master MOUS 2000