25% of syllabus · Time value of money, interest rates, force of interest, annuities and perpetuities.

Lemma · IAI CM1

Derivation-first CM1 prep that respects prerequisites

10 free lessons · master each atom before the next unlocks

Start Lesson 1

Your path through Theory of Interest Rates

12 lessons in one prerequisite chain. Master each stop to unlock the next — derivation-first, atom by atom.

The time value of money — intuition
Start
Build the intuition that money at different times is not directly comparable, and introduce accumulation and discount factors.
4 atoms · Free · Entry lesson
Compound interest mechanics
Open
Derive the compound accumulation formula from first principles.
3 atoms · Free · After lesson 1
Nominal interest rates and p-thly compounding
Open
Relate nominal and effective rates under p-thly compounding.
3 atoms · Free · After lesson 2
Force of interest (δ)
Open
Define the force of interest and connect it to continuous compounding.
3 atoms · Free · After lesson 3
Discounting a single cashflow
Open
Discount and accumulate single payments on a timeline.
3 atoms · Free · After lesson 4
Accumulating and discounting with varying interest rates
Open
Work with piecewise-constant and time-varying rates.
3 atoms · Free · After lesson 5
Real vs money interest rates
Open
Separate real and money rates using inflation.
3 atoms · Free · After lesson 6
The equation of value
Open
Set up equations of value for sets of cashflows.
4 atoms · Free · After lesson 7
Level annuity-immediate (aₙ)
Open
Derive the annuity-immediate formula from a geometric series.
3 atoms · Free · After lesson 8
Annuity-due (äₙ) and p-thly annuities
Open
Relate annuity-due and annuity-immediate; introduce p-thly annuities.
3 atoms · Free · After lesson 9
Deferred annuities (m|aₙ)
Open
Value annuities whose payments start after a deferral period.
3 atoms · Founding member · After lesson 10
Perpetuities and perpetuity-due
Open
Present values for infinite level payment streams and their due variants.
3 atoms · Founding member · After lesson 11

Loading…

Your path through Theory of Interest Rates

The time value of money — intuition

Compound interest mechanics

Nominal interest rates and p-thly compounding

Force of interest (δ)

Discounting a single cashflow

Accumulating and discounting with varying interest rates

Real vs money interest rates

The equation of value

Level annuity-immediate (aₙ)

Annuity-due (äₙ) and p-thly annuities

Deferred annuities (m|aₙ)

Perpetuities and perpetuity-due

Your path through Theory of Interest Rates

The time value of money — intuition

Compound interest mechanics

Nominal interest rates and p-thly compounding

Force of interest (δ)

Discounting a single cashflow

Accumulating and discounting with varying interest rates

Real vs money interest rates

The equation of value

Level annuity-immediate (aₙ)

Annuity-due (äₙ) and p-thly annuities

Deferred annuities (m|aₙ)

Perpetuities and perpetuity-due

Your path through Theory of Interest Rates

The time value of money — intuition

Compound interest mechanics

Nominal interest rates and p-thly compounding

Force of interest (δ)

Discounting a single cashflow

Accumulating and discounting with varying interest rates

Real vs money interest rates

The equation of value

Level annuity-immediate (aₙ)

Annuity-due (äₙ) and p-thly annuities

Deferred annuities (m|aₙ)

Perpetuities and perpetuity-due

Your path through Theory of Interest Rates

The time value of money — intuition

Compound interest mechanics

Nominal interest rates and p-thly compounding

Force of interest (δ)

Discounting a single cashflow

Accumulating and discounting with varying interest rates

Real vs money interest rates

The equation of value

Level annuity-immediate (aₙ)

Annuity-due (äₙ) and p-thly annuities

Deferred annuities (m|aₙ)

Perpetuities and perpetuity-due