Interest Formulas
The simple interest formula is:
I = Prt where I =
P=
r=
t=
Amount of interest
Principal
Annual interest rate (written as a decimal)
Time (in years)
The future value FV of a principal P invested at simple interest is:
FV = P(1+ rt)
The future value FV of a principal P invested at compound interest is:
FV = P(1+ i)n
Where r is the annual rate, m the number of compounding periods per year,
periodic rate i = r m , and n the total number of compounding periods.
For continuous compound interest:
FV = Pert , where e ≈ 2.71828 (the base of the natural logarithm).
m
r⎞
⎛
The annual percentage yield is: APY = ⎜ 1+ ⎟ − 1
⎝ m⎠
The future value FV of an ordinary annuity with payment size “pymt,” periodic
rate i, and a term of n payments is:
⎡ (1+ i)n − 1 ⎤
FV (ordinary) = pymt ⎢
⎥
i
⎣
⎦
The present value P of an ordinary annuity can be found from:
⎡ (1+ i)n − 1 ⎤
n
P(1+ i) = pymt ⎢
⎥
i
⎣
⎦