**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

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).