Calculating Annuity return : Back to basics

An annuity is a series of equal payments made in a specific interval over a period of time frame. This formula helps to calculate the future value of an annuity.

Formula:

        A = P * [ {(1+ i) ^ n - 1} / i ] * (1 + i )  -  when payment is made at the start
                                          or
       A = P * [ ((1+ i) ^ n - 1) / i ]       -   when payment is made at the end

      where
              A = final amount
              P = each equal payment
              i  =  interest rate for the interval ( in decimal)
              n =  the number of total payment made over the period.

Usage scenario:

• Return on PPF deposits made over 15 years.
• Return for mutual fund SIP done for a period of time.

Examples:

• What is the final return at the end of 15 years if Rs. 10000 is deposited every year?

          Here  P = 10000, i = .08, n =15

          Thus final amount, A = 10000 * [ {(1+.08)^15-1}/.08] * (1+.08)
                                         = 10000 * 27.15 * 1.08
                                         = 293242.8

• What is the final return for a Rs. 2000 monthly mutual fund SIP at the end of 3 years if annual return of the mutual fund is 15% ?

          Herein,  P = 2000
                       i  =  (15/12) = 1.25 % ~ 0.0125
                       n =  (12*3) = 36

           Thus final amount, A = 2000 * [ {(1 + .0125)^36-1}/0.0125] * (1 + 0.0125)
                                           = 2000 * 45.16 * 1.0125
                                           = 91358.9