Basic formulas
Interest paid after interest period
Simple interest (linear function):
FV = PV + I
I = PV ∗ r ∗ t
FV = PV (1 + r ∗ t)
where FV...Future V alue, PV....Present V alue, r....Interest Rate, t...Time,
I....Interest.
Compound interest (exponetial function):
FV = PV (1 + r)t
,
Note: here the time gives rather # of interest period.
Combined interest (compound + simple):
FV = PV (1 + r)n
(1 + r ∗ R),
where n....#number of whole interes periods (integer) and then the total time
is n + R, and R < 1, since 1 corresponds to one interest period. !!! If the
time is not the whole number of interest periods to reach the maximum you
should apply the combined interest. The utility can be maximized through FV
(more then from compound interest), PV (less then from CI) or the time will
be shorter! In the case to nd the time, the solution consists in two steps:
1. simply application of compound interest : FV = PV (1 + r)t
,
if the t is not an integer apply the second step:
2. FV = PV (1 + r)n
(1 + r ∗ R),
here the whole number of time will be applied in compound interest (in
exponent) and the only unknown remains the R, so then solve a simple equation
with one unknown (R).
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Interest paid ahead interest period
Simple interest (linear function):
PV = FV (1 − dt)
IT IS POSSIBLE TO DERIVE
ALL UNKNOWNS FROM GIVEN
EQUATIONS!
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