## TVM Techniques

There are broadly two TVM techniques, which are mirror images of each other:

Technique	Also Called	Direction in Time	Question it Answers
Future Value (FV)	Compounding	Today → Future	What is today's money worth later?
Present Value (PV)	Discounting	Future → Today	What is tomorrow's money worth now?

### 1. Future Value (Compounding Technique)

Future Value is the cash value of an investment at some point in the future. It is tomorrow's value of today's money, compounded at the rate of interest.

$$FV = PV \times (1 + r)^n$$

Where:

PV = present (today's) amount invested
r = rate of interest (per period, as a decimal)
n = number of periods

### 2. Present Value (Discounting Technique)

Present Value is today's value of tomorrow's money, discounted at the interest rate. It is simply the FV formula rearranged.

$$PV = \frac{FV}{(1 + r)^n}$$

### The Relationship

Compounding and discounting are inverse operations:

Compounding pushes money forward in time (multiply by $(1+r)^n$).
Discounting pulls money backward in time (divide by $(1+r)^n$).

The term $(1+r)^n$ is the compounding factor; its reciprocal $\frac{1}{(1+r)^n}$ is the discounting factor (PVF).

Worked example

### Example 1

Future Value: You invest ₹10,000 today at 8% p.a. for 3 years.

$$FV = 10{,}000 \times (1.08)^3 = 10{,}000 \times 1.259712 = ₹12{,}597.12$$

### Example 2

Present Value: You will receive ₹12,597.12 three years from now; the discount rate is 8%.

$$PV = \frac{12{,}597.12}{(1.08)^3} = \frac{12{,}597.12}{1.259712} = ₹10{,}000$$

Notice this is the exact reverse of the compounding example — confirming the two techniques are inverses.

⚠️ Common exam mistakes

Mixing up the formulas — dividing when you should compound (or vice versa). Remember: future value → multiply by (1+r)ⁿ; present value → divide by (1+r)ⁿ.
Using the interest rate as a whole number (e.g. 8) instead of a decimal (0.08) inside (1+r).
Forgetting to match the rate and the number of periods to the same compounding frequency (e.g. using an annual rate with a monthly period count).

Reference:

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TVM Techniques — Future Value (Compounding) vs Present Value (Discounting)

Worked example

⚠️ Common exam mistakes