← The Price of Waiting · Lesson 3 of 3
A small fee, a long time
A yearly fee is taken as a share, so it compounds too. Take the same 1,000 and an assumed 6% a year, but a 1% yearly fee, so it grows 5% a year instead.
After 30 years that is 1,000 × 1.05³⁰ ≈ 4,322, against 5,743 with no fee. One per cent a year has taken about a quarter of the end amount (1 − 4,322 ÷ 5,743 ≈ 0.25). A half-per-cent fee would take about 13%.
This lesson does not say which account to choose; it shows how to read a fee. On Spark & Anvil, teenagers work the same sum in The Fee That Grows.
A new example: at an assumed 6% a year, about what share of the 30-year amount would a 2% yearly fee take?
A lesson is kept once you've answered the question and written at least 8 words. Nobody grades it; it stays on this device.