Formula Lab

Every ICWIM calculation, one lesson at a time

25 lessons and 177 drills covering the calculations in the ICWIM syllabus, from interest rate parity to retirement need.

Most ICWIM material treats calculations as a list of formulas to memorise. That works until an exam question gives you the answer and asks for the rate, or gives you a payment at the start of the period rather than the end. Formula Lab is built the other way round: it starts with how you recognise which formula a question is asking for.

Lessons
25
Drills
177
Chapters covered
3, 5, 6, 8

How each lesson is built

Every one of the 25 lessons has the same six parts, in the same order.

  1. Recognition cues. The words in a question that tell you which formula it wants. This comes first because choosing the wrong formula confidently is the more expensive mistake.
  2. The formula, with each variable named.
  3. Method. The order to do things in, including the steps that are easy to do in the wrong sequence.
  4. A worked example with the numbers carried through.
  5. A sense check. One sentence telling you what a plausible answer looks like, so you can catch an answer that is wrong by a factor or a sign before you commit.
  6. Traps. The specific ways this calculation goes wrong.

Then the drills: six in every lesson except one short supplementary lesson, which has three. The drills deliberately do not all run the formula forwards: some give you the answer and ask for the rate or the number of years, because that is how a calculation becomes a test of understanding rather than of memory.

Two complete lessons

These two are shown in full so you can judge the format rather than take our word for it. The drills that follow them are part of the paid product.

Time Value of Money · Chapter 5

Present Value and the Rule of 72

Present value reverses compounding and tells you what a future amount is worth today.

Recognise it

  • present value
  • discounting
  • how much today
  • future lump sum
  • Rule of 72
  • doubling time

The formula

PV = FV ÷ (1+r)^n. Approximate doubling time ≈ 72 ÷ annual rate (%).

Method

  • For PV, discount the future amount by the growth factor.
  • For Rule of 72, use the percentage number, not the decimal.
  • Use Rule of 72 only as a reasonableness check.

Worked example

Need £80,000 in 8 years at 4%: PV = 80,000/1.04^8 ≈ £58,455.

Sense check

With a positive discount rate, PV must be below FV.

Where it goes wrong

  • Multiplying instead of dividing for PV.
  • Using 0.06 in 72 ÷ rate instead of 6.
  • Treating Rule of 72 as exact.

In Formula Lab this lesson is followed by six drills that mix the variations, so you meet the formula rearranged rather than always in the form you learned it.

Statistics & Risk · Chapter 5

Geometric Mean and Compound Average Return

The geometric mean gives the compound average rate implied by a sequence of returns.

Recognise it

  • geometric mean
  • compound average
  • average annual growth
  • multi-year returns

The formula

Geometric mean = [(1+R1)(1+R2)…(1+Rn)]^(1/n) − 1

Method

  • Convert each return to a growth factor.
  • Multiply the growth factors.
  • Take the nth root.
  • Subtract 1.

Worked example

+8%, −4%, +6% gives (1.08×0.96×1.06)^(1/3)−1 ≈ 3.19%.

Sense check

With volatile returns, geometric mean is normally below the arithmetic mean.

Where it goes wrong

  • Taking the ordinary average of the percentages.
  • Multiplying the percentage numbers instead of growth factors.
  • Forgetting to subtract 1.

In Formula Lab this lesson is followed by six drills that mix the variations, so you meet the formula rearranged rather than always in the form you learned it.

What Formula Lab covers

AreaLessonsDrills
Markets & Rates530
Statistics & Risk530
Time Value of Money636
Company Analysis & Valuation318
Portfolio Performance16
Financial Planning16
Mastery Extensions421
Mixed drills, across lessons030
Total25 177

A few of the lessons

Seven of the twenty five, to show the range rather than the whole list.

The full lesson list, the drills and the answer reasoning are part of the paid product.

How Formula Lab connects to the syllabus

Formula Lab covers four chapters. Chapter 3 has the forward rate using interest rate parity, plus bond yields and AER. Chapter 5 carries most of the rest, across statistics, financial mathematics and the ratio family. Chapter 6 adds portfolio return and the risk adjusted measures, and Chapter 8 asks you to calculate a retirement need.

See the question style for yourself

Fifteen questions from the bank, free, with the reasoning after each one.

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