Savings annuity calculator with graph

==============================================================================
 Period     Payment amount (PMT)     Interest earned (I)     Future value (FV)
==============================================================================
      1                    50.00                    0.00                 50.00
      2                   100.00                    0.25                100.25
      3                   150.00                    0.75                150.75
      4                   200.00                    1.51                201.51
      5                   250.00                    2.51                252.51
      :                       :                       :                     :
    295                 14750.00                18800.01              33550.01
    296                 14800.00                18967.76              33767.76
    297                 14850.00                19136.59              33986.59
    298                 14900.00                19306.53              34206.53
    299                 14950.00                19477.56              34427.56
    300                 15000.00                19649.70              34649.70

• Calculate the future value (FV) using equation:
  

  FV =	PMT * ((1 + R/N)N * T - 1)
  	R / N

  
  
  
• Calculate the periodic payment amount (PMT) using equation:
  

  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.
  
  
• Calculate the nominal interest rate (R) per year (as a decimal, not in percentage) using equation:
  

  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.
  
  
• Calculate the time period (T) in years using equation:
  

  T =	log((R / N) * ((FV / PMT) + (N / R)))	and	FV = N * T * PMT + I
  	N * log(1 + (R / N))

  
• Calculate the compounding periods (N) in one year using equation:
  

  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%).
  
  
• Calculate the effective interest rate (Re) per year (as a decimal, not in percentage) using equation:
  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.
  
  
• Let you specify the compounding period:
  
  • daily
    360, 364, 365 or 366 times per year
  • weekly
    52 times per year
  • bi-weekly (every two weeks)
    26 times per year
  • semi-monthly (twice a month)
    24 times per year
  • monthly
    12 times per year
  • bi-monthly (every two months)
    6 times per year
  • quarterly
    4 times per year
  • semi-annually (twice a year)
    2 times per year
  • yearly
    1 time per year
  
  
• Let you specify the time period in two ways:
  
  • Method 1: Enter the time period by number of: days, weeks, bi-weeklies, semi-monthlies, months, bi-monthlies, quarters, semi-annuallies or years.
  • Method 2: Enter a from date and to date. Both dates can also be included or excluded.
  
  
• Set the number of days in a year to 360, 364, 365 or 366 days.
  
  
• Draw two graphs in a single plot (see images above).
  • Graph 1: Future value (FV) - Month
  • Graph 2: Future value (FV) / Interest earned (I) - Month
  
  To show/hide a graph click the name in the plot legend.
  Press button "Make plot image" to create an image which can be saved.

Input savings annuity calculator with graph: Calculate: Future value (FV)Periodic payment amount (PMT)Nominal annual interest rate (R)Time period (T)Compounding period (N) Future Value (FV)*: Periodic payment amount (PMT): *: Nominal annual interest rate (R) *: %    per year Compounding period (N): dailyweeklybi-weekly (every two weeks)semi-monthly (twice a month)monthlybi-monthly (every two months)quarterlysemi-annually (twice a year)yearly Time period (T) *: daysweeksbi-weeklies (every two weeks)semi-monthlies (twice a month)monthsbi-monthlies (every two months)quarterssemi-annuallies (twice a year)years From / To date From date:    To date:    Include From / To date Include from date: Include to date:   Days in year: 360364365366 Chart: Stack bar chartLine chart   * = required