av David Kedrowski för 14 årar sedan
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r_eff = (1 + r/m)^m - 1
r_eff = APY (convert back to percent)
r = APR (convert to decimal)
m = conversion periods per year
Effective rate
APY
Equivalent simple interest rate (for one year)
P = Ae^(-rt)
A = future value (principal + interest) (dollars)
P = present value (dollars)
r = nominal interest rate (convert to decimal) (annual)
t = time (years)
P = A(1 + r/m)^(-mt)
A = future value (principal + interest) (dollars)
P = present value (dollars)
r = nominal interest rate (convert to decimal) (annual)
m = conversion periods per year
t = time (years)
Future value = accumulated amount
Present value = principal
These terms are tricky because they are really only relative to each other; that is, future value comes after present value in time.
When the variable is an exponent, logarithms must be used to bring the variable out of the exponent.
The relevant rule is
log_b m^n = n log_b m.
However, if the variable is in the base of an expression with a fixed exponent, we can use roots to help in isolating the variable.
The relevant rule, assuming m represents nonnegative values, is
(m^n)^(1/n) = m.
It is not practical for everyday interest calculations.
It is useful for certain theoretical work in finance.
It is also useful for quantities that don't increase at set intervals, like inflation and population growth.
A = Pe^(rt)
A = accumulated amount (principal + interest) (dollars)
P = principal (dollars)
r = nominal interest rate (convert to decimal) (annual)
t = time (years)
A = P(1 + r/m)^(mt)
A = accumulated amount (principal + interest) (dollars)
P = principal (dollars)
r = nominal interest rate (convert to decimal) (annual)
m = conversion periods per year
t = time (years)
We assume the conversion period is a constant length of time from one interest calculation to the next.
We represent the number of conversion periods in one year by the letter m.
Typical conversion periods are the following:
Nominal
Stated
APR
A = P(1 + rt)
A = accumulated amount (principal + interest) (dollars)
P = principal (dollars)
r = interest rate (convert to decimal) (annual)
t = time (years)
I = Prt
I = simple interest (dollars)
P = principal (dollars)
r = interest rate (convert to decimal) (annual)
t = time (years)
Simple interest is only ever accrued based on the original principal.
Typically a function of time, though it can be thought of as a function of principal or interest rate
