Calculated Industries Qualifier Plus IIIFx:
Logarithm, Exponential, Square Root
Introduction
Say
we have a financial calculator such as Calculated Industries
Qualifier Plus IIIFx (or the Pocket Real
Estate Master or another pocket basic financial calculator).
Note that this calculator does not
have the following functions: natural logarithm (ln x), exponential
function (e^x), and square root (√). No problem. We can use the
time value of money keys.
The
relationship between present value (PV), future value (FV), periodic
interest rate (I%), and number of periods (N) is determined as:
FV =
PV * (1 + I% / 100) ^ N
For
the natural logarithm and exponential, start by dividing both sides
by PV:
FV
/ PV = (1 + I% / 100) ^ N
Let
PV = 1 and equate 1 + I% / 100 = e (e ≈ 2.71828182846…)
Then:
1 +
I% / 100 = 2.71828182846
I% /
100 = 1.71828182846
I% =
171.828182846
Since
financial calculators are usually set to 2 decimal places, for most
instances, we can use the approximation with reasonable accuracy:
I% ≈
171.82818
Then
we have:
FV /
1 = (1 + 171.82818 / 100) ^ N →
FV ≈
e^N and ln FV ≈ N
Now
for square root:
Let’s
start with the same basic relationship:
FV
/ PV = (1 + I% / 100) ^ N
Let
PV = 1, and N be 0.5 since √x is x^0.5 for x≥0.
Let
x = 1 + I% / 100. Solving for I%:
x =
1 + I% / 100
x –
1 = I% / 100
100
* (x – 1) = I%
FV ≈
√x
FV /
1 = ((100 * (x – 1)) ^ 0.5
We
can use this to build similar relationships with powers and roots.
Procedures
and Examples
Procedure
for ln(x):
Set
the following variables:
P/Y
= 1
Loan
Amt = 1*
Int
= 171.82818
FV
= x
Solve
for Term
Estimate
ln 55.5.
P/Y
= 1
Loan
Amt = 1*
Int
= 171.82818
FV
= 55.5
Solve
for Term
Result
(Term): 4.02
Procedure
for e^x:
P/Y
= 1
Loan
Amt = 1*
Int
= 171.82818
Term
= x
Solve
for FV.
Estimate
e^2.
P/Y
= 1
Loan
Amt = 1
Int
= 171.82818
Term
= 2
Solve
for FV
Result
(FV): 7.39
Procedure
for √x:
P/Y
= 1
Loan
Amt = 1*
Term
= 0.5
Int
= 100 * (x – 1)
Solve
for FV
Example:
Estimate √84.
P/Y
= 1
Loan
Amt = 1
Term
= 0.5
Int
= 100 * (84
– 1) = 8300
Solve
for FV
Result
(FV): 9.17
*Note:
Loan Amt (PV) is entered as -1 on
graphing calculator TVM solvers.
Note:
Please do not try this on the HP 12C or the BA Plus II, because on
those calculators, the variable N is rounded up to the near highest
integer.
Enjoy
this hack and until next time,
Eddie
All
original content copyright, © 2011-2024. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
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