Inputs
Example scenarios
Click Load to populate the inputs with an example.
| Scenario | First payment | COLA % | Discount % | Defer yrs | Years | Freq | Timing | Action |
|---|---|---|---|---|---|---|---|---|
| Public pension baseline | ₨ 1,200,000 | 2.0 | 6.0 | 5 | 25 | Annual | End | |
| Immediate annuity due | ₨ 600,000 | 0.0 | 5.0 | 0 | 20 | Monthly | Begin | |
| High COLA moderate discount | ₨ 900,000 | 3.5 | 6.5 | 3 | 30 | Annual | End |
Results
₨ 0
Present value today
r=6.00% · g=2.00%
Ordinary
Annual
25 years
Deferred 5 yrs
Chart shows sensitivity of present value to the discount rate (±2 percentage points).
Formula used
We treat the pension as a growing annuity possibly deferred and with optional beginning-of-period payments.
Per-period rates:
r_p = (1 + r_annual)^(1/m) - 1
g_p = (1 + g_annual)^(1/m) - 1
m = payments per year (1 or 12)
Number of payments:
N = years × m
Deferral periods:
k = defer_years × m
Present value at time 0 (ordinary / end of period):
PV_0 = [ P1 × (1 - ((1+g_p)/(1+r_p))^N ) / (r_p - g_p) ] ÷ (1+r_p)^k
If payments are at the beginning of each period (annuity due):
PV_0_due = PV_0 × (1 + r_p)
Special case when r_p ≈ g_p:
PV_0 ≈ [ P1 × N / (1 + r_p) ] ÷ (1+r_p)^k
And PV_0_due ≈ PV_0 × (1 + r_p)
Payment schedule (first 24 rows)
| # | Period | Payment | Discount factor | Present value |
|---|