You can use formulas presented here: https://money.stackexchange.com/a/94307/11768
First calculating the size of the pension fund required.
p = ((1 + i)^o (1 + m)^-n ((1 + i)^n - (1 + m)^n) w)/(i - m) (formula 2)
where
n is the number of payments to be received
o is the number of the period at the end of which the first payment is received
w is the payment amount
m is the pension fund's periodic rate of return
i is the periodic inflation rate
With the following criteria
- time now is start of year 1
- final payment into pension pot at the end of year 20
- first retirement payment received at end of year 21
- final retirement payment received at end of year 50, totaling 30 payments
For example, with fund interest at 3% pa and inflation at 2% pa.
n = 30
o = 21
w = 60000
m = 0.03
i = 0.02
p = ((1 + i)^o (1 + m)^-n ((1 + i)^n - (1 + m)^n) w)/(i - m) = 2307538
Upon final payment into the fund, at the end of year 20, the fund should total $2307538 to support 30 subsequent payments of $60000 at today's value.
The first payment received, at the end of year 21, will be $90940, and the final payment, at the end of year 50, will be $161495.
w (1 + i)^21 = 90940
w (1 + i)^50 = 161495
Calculating monthly payments into the fund
Formula 4 is designed to expect an immediate first payment, i.e. at the start of period 1, and thereafter for q further periods, with the payments increasing to offset inflation.
d = ((i - m) p)/((1 + i)^(1 + q) - (1 + m)^(1 + q)) (formula 4)
where
d is the initial payment amount
m is the pension fund's periodic rate of return
i is the periodic inflation rate
q is the number of payment periods
The period is now monthly so converting interest and inflation.
m = (1 + 0.03)^(1/12) - 1 = 0.00246627
i = (1 + 0.02)^(1/12) - 1 = 0.00165158
q = 20*12 = 240
d = ((i - m) p)/((1 + i)^(1 + q) - (1 + m)^(1 + q)) = 5835.30
The first payment at the start of month 1 should be $5835.30.
There are 241 payments in this scheme.
The payments increase like so
end of month 1: d (1 + i) = 5844.94
end of month 2: d (1 + i)^2 = 5854.59
end of month 3: d (1 + i)^3 = 5864.26
. . .
end of month 240: d (1 + i)^240 = 8670.95
Alternatively, for 241 equal payments (also starting immediately) a simpler formula can be used
g = (m p)/((1 + m)^(1 + q) - 1) = 7021.04
