Final yr, after we revealed the Unified Pension Scheme vs Nationwide Pension Scheme Calculator, many readers have been shocked that we used a single formulation to find out future NPS corpus by treating it as a step-up SIP. Since then, a number of customers of that software have requested us to elucidate the formulation. So listed here are the small print.
A step-up SIP refers to periodic investments the place the invested quantity will increase at some fee. That is technically known as a rising annuity.
SIP formulation
- SIP = month-to-month SIP quantity. We will multiply this by 12 and think about the corpus from a yearly SIP. For the reason that returns are variable, the distinction between a month-to-month SIP and a yearly SIP is insignificant over time,
- n = no of years the funding is made
- r = anticipated fee of return (you’ll be able to account for taxes by suitably decreasing this worth)
Corpus = 12*SIP*[(1+r)^n-1]/r
funding made on the finish of every interval (yr on this case)
Corpus = 12*SIP*(1+r)*[(1+r)^n-1]/r
funding made firstly of every interval (yr on this case)
Right here ^ refers to, to the facility of. x^2 = x*x. 2^3 = 2*2*2 = 8
Step-up SIP formulation
Now, we embrace one other variable
- g – the speed at which investments improve annually. For instance, if g = 10%, and the preliminary month-to-month SIP quantity is Rs. 1000. After one yr, the SIP quantity is Rs. 1100 and so forth.
Corpus = 12*SIP*[(1+r)^n- (1+g)^n]/(r-g)
funding made on the finish of every interval (yr on this case)
Corpus = 12*SIP*(1+r)*[(1+r)^n- (1+g)^n]/(r-g)
funding made firstly of every interval (yr on this case)
What if g > r?
Many readers marvel if this formulation will work if g >r. The corpus won’t change into unfavourable. It’s because when g>r, the issue [(1+r)^n- (1+g)^n] is unfavourable. However (r-g) within the denominator can also be unfavourable and the indicators cancel off.
There may be, nonetheless, one problem on this formulation.
What if r =g? Then, the denominator turns into zero, and we’ll get a 1/0 zero error, often known as a singularity in math.
When r=g, the next formulation applies for a step-up SIP
Corpus = 12*SIP*n*(1+r)^(n-1)
funding made on the finish of every interval (yr on this case)
Corpus = 12*SIP*n*(1+r)^n
funding made firstly of every interval (yr on this case)
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