Time Value of Money | Lightship Wealth Strategies, Inc.

Welcome, New Associates!

Facilitator: Tristan Ryan

Today isn’t just a lesson in formulas — it’s about unlocking how money actually works over time. This is one of the most important building blocks in financial planning. If you can master this, you’re 80% of the way to understanding how we model financial decisions for our clients.

Quick Poll: Before we start, how comfortable are you with TVM?

Part 2: The Core Concepts of TVM

The foundational idea: A dollar today is worth more than a dollar tomorrow, because it can be invested and earn a return.

The 5 Key Variables

PV (Present Value): Your starting point. The lump sum of cash you have right now.

FV (Future Value): The finish line. What your money could become after time and growth.

N (Number of Periods): The runway. The amount of time for growth. Crucially, the period (years, months, etc.) must match the rate and payment frequency.

R (Rate of Return): The engine. The growth rate for each period. (Note: This is a nominal rate. For true purchasing power, we often adjust for inflation).

PMT (Payment): Regular fuel-ups. A repeating series of contributions or withdrawals.

The Formulas, Demystified

FV = PV * (1 + r)ⁿ

In English: This formula tells you how a single lump sum grows. We take your Present Value (PV) and multiply it by a 'growth factor' of `(1 + r)`. The `ⁿ` (to the power of n) is the magic of compounding—it applies that growth factor over and over again for each period.

FV of Annuity = PMT * [((1 + r)ⁿ - 1) / r]

In English: This formula finds the future value of a series of equal payments. Pro Tip: This is where mistakes happen! If your `PMT` is monthly, your `r` must be the monthly interest rate (annual rate / 12) and `n` must be the total number of months (years * 12).

See How They Interact

Present Value (PV)

Annual Rate (r) %

# of Years (n)

Future Value (FV) is:

Visualizing The Growth

Part 3: The Power of Starting Early

Meet Alex, the Early Bird, and Ben, the Late Bloomer.

Alex starts saving at age 25. Ben waits until 40 but tries to catch up by saving a much larger amount. Who wins the race to $1 million? Use the tool to find out.

Scenario 1: Alex, the Early Bird

Starts saving at 25.

Scenario 2: Ben, the Late Bloomer

Starts saving at 40.

Alex's Journey

Start Saving at Age: 25

Monthly Savings: $500

Assumed Annual Growth Rate: 7.0%

Reaches $1,000,000 at

Age 62

with a total contribution of $222,000

The rest is all investment growth!

Deeper Dive: The Cost of Waiting, Quantified

In our default scenario, Alex (starting at 25, saving $500/mo) invests a total of $218,500 over 37 years to become a millionaire at age 62.

To reach $1M by the same age, Ben (starting at 40) would need to save $1,600 per month. His total contribution would be $424,000.

By waiting 15 years, Ben has to contribute almost double out of his own pocket to get to the same place. Alex's money had more time to compound, so their growth did the heavy lifting.

Part 4: Solve Real Client Cases

Let's apply what you've learned. Click to reveal the variables, then check your thinking against the step-by-step solution.

The Cardinal Rule of TVM

Always match your period rate (R) and number of periods (N) to the payment frequency (PMT)! If payments are monthly, your rate and periods must also be monthly. This is the most common mistake new associates make.

Case Study 1: The Retirement Gap

A 55-year-old client wants to retire in 10 years. They have $750,000 saved and contribute $1,500/month. Their goal is $1.5M. Assuming a 6% annual return, will they make it?

PV:$750,000[Click to reveal]
PMT:$1,500[Click to reveal]
N:120 Months (10 years)[Click to reveal]
R:0.5% (6% annually)[Click to reveal]
FV: ?

Case Study 2: The Education Goal

A new parent wants to have $200,000 for their child's college in 18 years. How much do they need to invest today in one lump sum to reach that goal, assuming a 7.5% annual return?

FV:$200,000[Click to reveal]
PMT:$0[Click to reveal]
N:18[Click to reveal]
R:7.5%[Click to reveal]
PV: ?

Case Study 3: Solving for Rate

A client has $250,000 and wants it to grow to $500,000 in 7 years for a down payment, without adding new savings. What annual rate of return (r) must they achieve?

PV:$250,000[Click to reveal]
FV:$500,000[Click to reveal]
PMT:$0[Click to reveal]
N:7[Click to reveal]
R: ?

Part 5: Application & Knowledge Check

Where You'll Use TVM at Lightship

This isn't just theory. You will use these concepts every single day to provide clients with clarity and confidence. Here are a few examples:

Modeling retirement projections to answer "Am I on track?"
Calculating the lump sum a client needs to invest today for a future goal (like college).
Evaluating a client's pension offer (lump sum vs. annuity payments).
Showing a client the long-term impact of different savings rates.
Demonstrating how portfolio fees erode returns over time (the 'r' variable!).
Determining if a client's return expectations are realistic for their goals.

Check Your Understanding

1. If you invest $5,000 today at a 10% annual return, what will it be worth in 5 years?

Correct! The formula is FV = $5,000 * (1 + 0.10)^5. Compounding adds an extra $552.55 over simple interest.

2. Holding all else equal, what change results in the HIGHEST future value?

Correct! Because time (n) is an exponent, doubling it has a much more dramatic effect due to compounding than doubling the other variables.

3. The process of finding out what a future sum of money is worth today is called:

Correct! We "discount" a future value back to the present to find its PV. Compounding is the process of growing a present value into a future value.

4. To double your money in 10 years, you need an approximate annual return of:

Correct! This is a classic application of the "Rule of 72," a great mental shortcut. 72 / 10 years = 7.2% required return.

Final Challenge

Would you rather have:

A) $1,000,000 today

B) A penny that doubles in value every day for 30 days?

Your True Final Challenge

"Try to explain TVM to someone at dinner tonight. If you can teach it, you get it."

Lightship Wealth Strategies

Time Value of Money (TVM) Training