The time value of money — intuition | time value of money

Money paid at different dates is not the same economic object. Rs. 1,000 today and Rs. 1,000 in one year are both certain — yet no rational borrower would swap them one-for-one. The time value of money (TVOM) is the principle that cashflows must be translated to a common date before we compare, add, or rank them.

Actuarial work always picks two directions of translation:

Accumulation (or capitalisation): move money forward in time.
Discounting: move money backward in time.

We write $t$ for time measured in years from a reference date (usually $t=0$ “now”). A payment at time $t$ is a cashflow; plotting cashflows on a timeline is not decoration — it fixes the exponent in $(1 + i$ .

Prerequisites

Teach

Why comparison requires a rate

Conventions we keep for CM1

Worked example: Comparing two certain offers

Worked example: Timeline and present value

Comparing offers by present value

Worked example: Which offer wins?

Worked example: Three payment times

What mastery requires

Practice

Practice 1

Practice 2

Practice 3

Practice 4

Practice 5

Practice 6

Practice 7

Practice 8

Practice 9

Practice 10

Practice 11

Practice 12

Synthesis practice

Practice 1

Practice 2

Mastery checks

Time value concept

Check 1

Check 2

Check 3

Accumulation and discount factors

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Cashflow timelines

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)

Comparing offers by present value

Check 1(Complete prior skills first)

Check 2(Complete prior skills first)

Check 3(Complete prior skills first)