Savings annuity calculator with graph help


Settings Remark
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.