Methodology
The net present value today of the pension you will receive over your lifetime is given by the following equation:
where
p is the current value of the State pension
D is the number of years until death
T is the number of years until the State pension commences (chosen start date)
b is the bonus for waiting an extra year
r is the real real rate of return on savings (assuming they are continuously compounded)
In the situation where r=0, by setting it can be shown that optimum time to defer the State Pension (T*) is given by:
In the general case, where r is non-zero, by setting it can be shown that:
This equation cannot be solved analytically in terms of T*, but since |F”(T*)/F'(T*)|<1 – where F(T*) is the above equation set to zero – the calculations use the Newton-Raphson numerical method to find an iterative solution. With a suitably chosen initial estimate of T*(we use 1) this rapidly converges on a solution (the calculation uses only three steps).