Time Value of Money Concepts

Time Value of Money (TVM) is one of the most heavily tested topics on the CFP exam. Expect numerous calculation questions across retirement planning, education funding, and investment analysis. Mastering TVM is essential because virtually every financial planning calculation builds on these fundamental concepts.

The Core Principle: Why Money Has Time Value

A dollar today is worth more than a dollar in the future. This fundamental principle underlies all of financial planning. Two key factors drive this concept:

Understanding this principle helps explain why clients should start saving early, why interest rates affect borrowing decisions, and why future retirement needs must be calculated in today's dollars.

The Five TVM Variables

Every TVM calculation involves five variables. On your financial calculator (HP 12C or Texas Instruments BA II Plus), these are represented by specific keys:

The Golden Rule of TVM Calculations: To solve for any one variable, you must know the other four. If you are given four variables, you can always calculate the fifth.

Exam Tip: The CFP exam allows specific financial calculators. Practice extensively with the HP 12C or TI BA II Plus. Speed and accuracy with your calculator are essential.

Understanding Compounding and Discounting

TVM calculations move money through time in two directions:

Compounding (Moving Forward in Time)

• Starts with PV, calculates FV
• Answers: "What will this amount grow to?"
• Uses formula: FV = PV x (1 + i)^n

Discounting (Moving Backward in Time)

• Starts with FV, calculates PV
• Answers: "What is this future amount worth today?"
• Uses formula: PV = FV / (1 + i)^n

Calculator Sign Conventions

This is where many candidates make errors. Financial calculators require consistent sign conventions:

• Cash Inflows (money coming TO you): Enter as POSITIVE
• Cash Outflows (money going FROM you): Enter as NEGATIVE

Always think from the perspective of the client or the investor.

Compounding Frequency

Interest can compound at different frequencies, and more frequent compounding produces higher returns:

Key Calculator Settings:

• P/Y: Payments per year
• C/Y: Compounding periods per year

When payment frequency differs from compounding frequency, ensure both settings are correct. For most exam problems, P/Y and C/Y are the same (e.g., both set to 12 for monthly calculations).

Exam Tip: Always check your P/Y and C/Y settings before starting a problem. Enter interest rates in percentage form (enter "6" for 6%, not "0.06").

Real vs. Nominal Returns

When planning for long-term goals, you must account for inflation:

Approximation Formula: Real Return = Nominal Return - Inflation Rate

Precise Formula: Real Return = [(1 + Nominal) / (1 + Inflation)] - 1

Example: If investments earn 8% and inflation is 3%:

• Approximate real return: 8% - 3% = 5%
• Precise real return: (1.08 / 1.03) - 1 = 4.85%

Practical Example: Future Value of a Lump Sum

Problem: Your client has $50,000 to invest today. If the expected return is 7% annually, what will this investment be worth in 15 years?

Calculator Inputs:

• N = 15 (years)
• I/Y = 7 (annual rate)
• PV = -50,000 (outflow, money leaving client)
• PMT = 0 (no additional contributions)
• Solve for FV = ?

Solution: FV = $137,951.94

The investment nearly triples due to compound growth over 15 years.

Practical Example: Present Value of a Future Amount

Problem: Your client needs $250,000 in 10 years for their child's education. If they can earn 6% annually, how much must they invest today as a lump sum?

Calculator Inputs:

• N = 10
• I/Y = 6
• PMT = 0
• FV = 250,000 (positive, money client will receive/need)
• Solve for PV = ?

Solution: PV = -$139,598.40 (the negative indicates an outflow, the client must invest this amount today)

The Rule of 72

For quick mental calculations, the Rule of 72 estimates how long it takes money to double:

Years to Double = 72 / Interest Rate

This rule is useful for quick client conversations and verifying calculator results.

Common TVM Exam Question Types

1. Future Value of Investment - How much will savings grow to?
2. Present Value of Goal - How much must be invested today?
3. Required Rate of Return - What return is needed to reach a goal?
4. Time Horizon - How long until a goal is reached?
5. Required Payment - What periodic contribution is needed?

Each question type solves for a different variable while the other four are given.