Exercise 1: Extending the Time Horizon From 20 to 30 Years — Possible Solution
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Using the chapter's own formula with P=£10,000, i=0.07, and n=30:

FV = 10000 x (1.07)^30
   = 10000 x 7.612272
   = approximately £76,123

This chapter's own 20-year figure was approximately £38,697. The
30-year figure of approximately £76,123 is roughly 1.97 times larger -
almost exactly double - even though the time horizon only increased by
50% (from 20 years to 30 years, i.e. 10 more years added to an existing
20).

WHY THE GROWTH ACCELERATES LIKE THIS
This is compounding's own defining feature: growth is applied to an
ever-larger base each year, not to the original £10,000 alone. The
extra 10 years (from year 20 to year 30) alone multiplies the existing
20-year balance by another factor of 1.07^10 (approximately 1.967) -
almost the same multiplier that applied to the very first 10 years,
even though the balance being multiplied is now nearly four times
larger than it started. In other words, the rate of proportional growth
per decade stays roughly constant, but because it's being applied to a
steadily growing balance, the absolute pound-value growth in each
successive decade is dramatically larger than the decade before it.

WHY THIS MATTERS
This is the real, concrete reason long-term investors are consistently
told that time in the market matters more than almost any other single
factor - the difference between investing for 20 years and investing
for 30 years isn't merely 50% more growth, it's nearly double, purely
from letting compounding run for one additional decade.

ANSWER: £10,000 invested at 7% for 30 years grows to approximately
£76,123 - nearly double this chapter's own 20-year figure of £38,697,
even though the time horizon only increased by 50%. This demonstrates
compounding's own accelerating nature: growth is applied to an
ever-larger balance each year, so each additional decade contributes
proportionally more in absolute pounds than the decade before it,
which is exactly why a longer investing time horizon is disproportionately
valuable.

WHY THIS WORKS AS AN ANSWER
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This correctly recomputes the real formula for a 30-year horizon,
compares the result against the chapter's own 20-year figure, and
explains the underlying reason the growth is disproportionately larger
rather than simply describing the bigger number.