Exercise 3: Recalculating the Retirement Pot at £250/Month — Possible Solution
====================================================================

Using this capstone's own real formula with C=£250/month, i=0.069/12,
and n=360 months (the same real 6.9% net return and 30-year horizon
already established for the retirement pot):

FV = 250 x [(1.00575^360 - 1) / 0.00575]
   = 250 x [(7.876547 - 1) / 0.00575]
   = 250 x [6.876547 / 0.00575]
   = 250 x 1195.9207
   = approximately £298,980

This capstone's own real figure at £300/month was approximately
£358,776. The real difference:

£358,776 - £298,980 = approximately £59,796

WHAT THIS COMPARISON SHOWS
Comparing the two contribution amounts as a ratio: £250 is 250/300, or
approximately 83.3%, of £300. Comparing the two resulting final
balances the same way: £298,980 is also approximately 83.3% of
£358,776. These two ratios match almost exactly.

WHY THIS HAPPENS
This reveals a real, precise mathematical relationship: with the
interest rate and time period both held fixed, the final value produced
by this formula is directly proportional to the monthly contribution
amount. Reducing the monthly contribution by a given percentage reduces
the final balance by that exact same percentage, because the monthly
contribution amount (C) is simply a multiplying factor in the formula -
every other part of the calculation (the rate-driven growth factor)
stays completely unchanged regardless of how much is actually
contributed each month.

WHY THIS IS GENUINELY USEFUL TO KNOW
This is a real, practical planning tool: an investor can directly scale
a known projection up or down without recalculating the entire formula
from scratch. If £300/month over 30 years at 6.9% produces
approximately £358,776, then any other monthly contribution amount at
the same rate and time period can be found simply by applying the same
proportional ratio - a genuinely useful shortcut once the base
calculation has already been done once.

ANSWER: At £250/month instead of £300/month, over the same 30 years at
a net 6.9% return, the retirement pot would reach approximately
£298,980 - about £59,796 less than the £358,776 figure at £300/month.
This comparison shows that reducing the monthly contribution to
approximately 83.3% of its original amount produces a final balance
that is also approximately 83.3% of the original result - revealing
that, with the rate and time period held fixed, the final value this
formula produces is directly proportional to the monthly contribution
amount, since the contribution simply multiplies an otherwise unchanged
rate-driven growth factor.

WHY THIS WORKS AS AN ANSWER
------------------------------
This correctly recalculates the real formula at the new contribution
amount, identifies the precise proportional relationship between the
two contribution amounts and their resulting balances, and explains
the underlying mathematical reason (the contribution acting as a linear
multiplier) that produces this exact proportionality.