Planning for Multi-Year Goals – Time Value of Money Part 2

Continuing this series on concepts gleaned from my CFP® professional education, this installment is for anyone looking to improve their finances by planning ahead for big, multi‑year goals. We will use education funding to illustrate the idea, but the same principles apply to estimating retirement savings needs and other long‑term goals.

In short: we want to put a dollar price tag on how much it costs TODAY to fund future multi-year goals. That way we have a specific amount we can target our savings and investments toward.

🎈 Step One: Inflate

The first thing to consider with future goals is the impact of inflation. Prices in the economy increase over time, and while that might not be noticeable when budgeting for expenses a couple of months away, it matters a lot when your child is 2 and you are planning for college 16 years from now.

Using college tuition as an example, we know the cost today, but we do not know exactly what the cost will be in 16 years. We can estimate it by taking today’s cost and growing it each year by an assumed inflation rate. This ties into a core concept in finance called the time value of money.

Example

Current annual tuition: 30,000 dollars
Time until college: 16 years
Assumed inflation rate: 3 percent per year

We can estimate future tuition like this:

Tuition next year: 30,000 × 1.03 = 30,900
Tuition in 2 years: 30,000 × 1.03 × 1.03 = 31,827
Tuition in 3 years: 30,000 × 1.03³ = 32,782

For each year into the future we project the price, we need to apply one plus the inflation rate. We can use exponents for shorthand, and continue to add years of inflation acceleration up to our goal horizon of 16 years.

A financial calculator or online time value of money calculator makes this easy. For TVM problems, we usually work with five variables:

N = number of periods (years in this case)
I/Y = interest rate (inflation rate in this case)
PV = present value (today’s cost)
PMT = periodic payment (if making regular contributions we could put a number here, but we’ll assume zero for now)
FV = future value after N periods (what we are solving for here)

Plugging in the numbers with N = 16, I/Y = 3, PV = −30,000, PMT = 0, the calculator shows that 30,000 dollars today becomes 48,141 dollars after 16 years.

That gives us an estimate of year‑one tuition at our target school when our 2‑year‑old turns 18.

🤓 NOTE: In TVM math, present value and future value usually have opposite plus or minus signs. A positive value represents a cash inflow and a negative value represents a cash outflow. This convention comes from loan calculations. For example, if we took out a 16-year loan for $30k (borrowing money = cash inflow “+”) at 3% interest compounded annually (with no payments until maturity), after 16 years we would owe $48,141 back to the lender (paying money = cash outflow “-“).

Don’t get too caught up in the +/- signs, just remember to use opposite signs for PV and FV or the calculation won’t work.

🔧 Step Two: Adjust

We now have an estimate of the first year’s tuition when our adorable 2 year-old turns 18: $48,141. Next, we need to account for a few important details:

Tuition is due at the beginning of each term.
Most degree programs are four years, and tuition is likely to keep rising each year.
We have the opportunity to invest between tuition payments and hopefully earn a positive return.

The easiest way I’ve found to understand problems like this is to draw simple pictures.

In finance, a stream of payments is known as an annuity. When payments occur at the end of each period, it is a regular annuity; when payments occur at the beginning, it is called an “annuity due”. Because tuition is due upfront each year, we treat it as an annuity due and calculate the present value of that stream of payments right before college starts.

We’ll use our financial calculator just like step one, but we need to enter new values:

Using an inflation‑adjusted interest rate

To factor in the effects of both inflation and investment returns between payments, we’ll use an inflation‑adjusted interest rate for I/YR in this step. To calculate the rate we start with our assumed return on investment and reduce it by the assumed inflation rate:

Expected investment return: 6 percent per year
Inflation rate: 3 percent per year

A simple approximation would be: 6 − 3 = 3 percent real return. A more precise way is:

(1.06 ÷ 1.03) − 1 = 2.91 percent real return

This better reflects that inflation and investment returns are both compounding over time.

Setting up the calculator

In step one we were bringing current costs FORWARD through time to a future value to account for inflation. We knew the value today, we wanted the future value.

In step two we are bringing future costs BACKWARD. We want to estimate the total value of four years of tuition payments and have it on-hand at the START of the first year of college. Then we can sleep well knowing we saved enough for Junior’s educations.

So we need to calculate the present value (PV).

To find the total cost of four years of inflation‑adjusted tuition, we enter:

N = 4 (four years of tuition)
I/Y = 2.91 (inflation-adjusted return we calculated in the last step)
Payment (PMT) = −48,141 (our year‑one tuition estimate from step 1, “-” sign = a cash outflow)
FV = 0 (we don’t need money left over after the last tuition payment)
Payment timing: BEGINNING of each period (annuity due)

Solving for PV gives us $184,543. This is the total amount we need at the start of year 17 to afford four years of tuition, assuming a 6 percent investment return and 3 percent inflation.

If we can save up this amount after 16 years (by the BEGINNING of year 17), and invest at a 6% return between tuition payments, we can afford four years of college.

Notice the power of time-value of money calculations – we can bring prices FORWARD (FV) or BACKWARD (PV) in time. Kind of like time travel.

Pretty cool.

📈 Step Three: Invest

Now we turn the problem around: how much do we need to save and invest each year over the next 16 years to reach that $184,543‑dollar target?

We have 16 years to save up the amount needed for our little one’s college education. Depending on our budget and cash flow situation, we can set whatever savings goal makes sense for us – annual, monthly, etc. We’ll use annual savings here to illustrate.

Again, we’ll use our trusty financial calculator to crunch the numbers, but we’ll need to enter new values for N, I/YR, PV, FV and PMT.

This is a future goal and we’ll assume we will fund our annual savings after taking care of our normal living expenses, we’ll change the settings to apply payments at the END of each period.

Time until college: 16 years
Expected return on investments: 6% per year. Depending what investments we choose, this return could be higher or lower. Read this article for more.
Target future value: $184,543 (our answer from step 2)
Current savings for this goal: Let’s assume we haven’t saved anything yet (zero)
Contributions: at the end of each year

In calculator terms:

N = 16
I/Y = 6
PV = 0
FV = 184,543
Payment timing: end of each period

Solving for PMT gives an annual savings requirement of $7,188. If we save that amount at the end of each year for 16 years and earn 6 percent annually, we end up with enough to pay for four years of college under these assumptions.

We can calculate the goal in monthly terms as well by simply changing the N and I/YR inputs:

N = 16 × 12 = 192 months
I/Y = 6 ÷ 12 = 0.5 percent per month

Running the numbers this way yields a savings target of $575 per month, or $6900 per year. Why is it lower than the annual savings amount we calculated above?

Because if we contribute to our goal each month, those savings have more time to earn the investment return during the year. So we reach our goal faster with more frequent contributions. 🧠

Pulling It All Together

Let’s review our three step process for estimating multi-year savings goals:

Inflate: $30,000 dollars of tuition today grows to $48,141 in 16 years at 3 percent inflation.
Adjust: To cover four years of tuition starting at $48,141 and rising with inflation, we need $184,543 dollars set aside by year 17, assuming we can earn a 6% return (or better) on our investments.
Invest: To build up 184,543 dollars over 16 years, we need to save $7,188 dollars per year, or $575 dollars per month, and earn 6% (or better) on our investments.

Once you have these targets, you can compare them to your current budget and cash flow to see whether the goal is realistic or whether you need to adjust assumptions, timelines, or school choices.

The next step is to open the appropriate investment account and start putting a plan into action—kids grow up fast.

We Can Help

If you are unsure whether your current savings plan is on track for college or other long‑term goals, consider working with a professional advisor to run a time‑value‑of‑money analysis of your financial goals. At Financial Empowerment we help clients solve these types of problems every day.

Contact us today and we’ll help make sure you’re on track.

Thank you for reading.

🙏💵🙌