Older Financial Calculators: Using the TVM Solver for LN(x) and EXP(x)
Background and the Mathematics
Older and even some modern financial calculators do not have logarithm and exponential functions (ln, e^x). However, the time value of money keys can be used to find exponentials and logarithms, as first mentioned by Hewlett Packard's HP-80 Application Note 80-007 (see Source below).
Note the time value of money equation below:
FV = PV × (1 + I÷100)^n
where:
FV = future value (Final)
PV = present value (1st Amt/Loan)
I = periodic interest rate (Int)
PMT = payment
n = number of payments (# pmts, term)
P/Y = 1 (set payments per year 1)
Let PV = 1. Then:
FV = (1 + I÷100)^n
Let base = 1 + I÷100. Then:
FV = base^n
And:
log_base(FV) = n
log FV ÷ log base = n
Time Value of Money Setup
n = exponent
I = (base - 1) × 100
PV = -1*
PMT = 0
FV = (1 + I÷100)^n
For logarithm, enter FV and solve for n.
For exponentials, enter n and solve for FV.
e^x, ln x: set I = 171.8281828...
10^x, log x: set I = 900
b^x, log_b(x): set I = (b - 1) × 100
Examples
e^5.86 ≈ 350.7228
n = 5.86
I = 171.828
PV = -1 (+1 for calculators that do not follow the cash flow convention)
PMT = 0
Solve for FV
ln(376) ≈ 5.9296
I = 171.828
PV = -1 (+1 for calculators that do not follow the cash flow convention)
PMT = 0
FV = 376
Solve for n
Caution
This is works well for most financial calculators such as HP-80, HP 12C Classic, TI Personal Brother, Casio FC-100, Calculated Industries Qualifier Plus III FX 3430, and the HP 17BII+. However, on some calculators, such as HP 12C Platinum, round calculations for n, so logarithm calculations will not be accurate.
Source
Hewlett Packard. HP-80 Application Notes: Calculating Logs, Anti-Logs, And Roots of Numbers No. 80-007. December 10, 1973.
Eddie
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