Calculate

The savings annuity calculates the future value of a stream of equal payments made at regular intervals over
a specified period of time at a given interest rate.
FV =

PMT * ((1 + R / N)^{N * T}  1)

or

FV = 
PMT * ((1 + r)^{N * T}  1)

R / N

r

FV = N * T * PMT + I = A + I
r = R / N
where:
FV = Future value
I = Interest amount
A = Total payment amount
R = Nominal interest rate per year (as a decimal, not in percentage)
r = Interest rate per period (as a decimal, not in percentage)
T = Time period in years
N = Number of compounding periods in one year
PMT = Periodic payment amount, paid at the end of each payment period
Other variations of the savings annuity equation are used to calculate:
 The future value (FV)
FV =

PMT * ((1 + R/N)^{N * T}  1)

R / N

 The periodic payment amount (PMT)
PMT =

FV * (R/N)

and

FV = N * T * PMT + I

(1 + (R / N))^{N * T} 1

Note:
A sinking fund is when we know the future value of the annuity and wish to calculate the periodic payment amount.
 The nominal annual interest rate (R) (as a decimal, not in percentage)
FV

=

(1 + (R / N))^{N * T}  1

PMT

R / N

Note:
Keep substituting different values for R until we get successively closer to the desired value of FV / PMT.
 The time period (T) in years
T =

log((R / N) * ((FV / PMT) + (N / R)))

and

FV = N * T * PMT + I

N * log(1 + (R / N))

 The compounding periods (N) in one year
N =

log(((FV * r) / PMT) + 1)

and

FV = N * T * PMT + I

T * log(1 + r)

Note:
r = interest rate per period
For example, if you borrow $1000 for 2 years at 12% interest compounded quarterly, you must divide the annual interest rate by 4 to obtain the interest rate per period (r = R / N = 12 / 4 = 3%).
 The effective interest rate (Re) (as a decimal, not in percentage)
Re = (1 + (R / N))^{N}  1
or
Re = (1 + r)^{N}  1
Note:
The effective interest rate is the equivalent rate of compound interest earned over a period of one year
for a nominal interest rate per year which is compounded twice or more over the year.
