Six worked examples from practice.

1. Roth IRA started at 25

A graduate fresh out of school maxes the Roth IRA contribution limit ($7,000 in 2026) for 40 years and stops at 65. Assume a 7 % annual return, monthly compounding, contributions made at the beginning of each month.

• Inputs: P=0, r=7%, t=40, n=monthly, PMT=583.33, timing=begin
• Future value at age 65: $1,549,000 (rounded)
• Total contributed: $280,000. Interest earned: $1,269,000.

The interest share is 82 %. This is the textbook case for starting early. Note that the 7 % return assumption is a long-run equity-heavy portfolio average; a realistic glidepath that de-risks toward bonds in later years would produce a lower number, perhaps closer to $1.1M.

2. 529 college savings plan from birth

New parents open a 529 plan when their child is born and contribute $400/month for 18 years, targeting a four-year private undergraduate degree.

• Inputs: P=0, r=6%, t=18, n=monthly, PMT=400
• Future value at age 18: $155,000
• Total contributed: $86,400. Interest earned: $68,600.

That covers a meaningful share but not all of a $300K+ private four-year sticker price. Most planners pair this with an explicit conversation about state-school alternatives or sibling-coverage strategies. The 6 % return assumption is intentionally lower than the IRA example: 529 portfolios usually de-risk aggressively in the final five years.

3. Emergency fund in a high-yield savings account

A household keeps a $30,000 emergency fund in an HYSA paying 4.25 % APY (which is roughly 4.16 % nominal compounded daily). They make no contributions; the balance just sits.

• Inputs: P=30000, r=4.16%, t=5, n=daily, PMT=0
• Future value at 5 years: $36,920
• Interest earned: $6,920.

The point of an emergency fund is not return; it is liquidity. But a 4 %+ HYSA rather than a checking account paying 0.05 % adds real money over five years, and the funds remain available within one business day.

4. Credit card debt growing in the wrong direction

A $12,000 credit-card balance at 24 % APR with daily compounding, minimum payments only (assume the minimum just covers interest, no principal reduction). Project the “balance” if the holder were paying nothing for three years.

• Inputs (treating the rate as growth): P=12000, r=24%, t=3, n=daily, PMT=0
• Balance at 3 years: $24,650

The same compounding mechanism that makes 25-year savings plans work also makes 24 % credit-card debt double in just over three years. This is the case for treating high-interest debt as the highest-priority financial action, ahead of any investment that does not have a guaranteed ~24 % return.

5. Retirement catch-up at 50

A late starter realises at age 50 that they have $40,000 in a 401(k) and 15 years until target retirement. They begin maxing the contribution limit including the catch-up bonus — about $30,500/year in 2026 = $2,541/month.

• Inputs: P=40000, r=6%, t=15, n=monthly, PMT=2541
• Future value at 65: $830,000
• Total contributed: $497,400. Interest earned: $292,600.

A late start is not catastrophic, but the interest share drops to 35 % (vs. 82 % in scenario 1). Most of the future value here came from the contributions themselves. The mechanism we are exploiting is no longer compounding time; it is contribution capacity.

6. Inheritance windfall held vs. spent

A 35-year-old inherits $75,000. Two scenarios: invest in a balanced index portfolio (assume 6 %) for 30 years vs. spend it. The opportunity cost:

• Inputs: P=75000, r=6%, t=30, n=monthly, PMT=0
• Future value at 65: $453,000

If the spent alternative is a $75,000 home down payment that prevents 30 years of rent (call it $1,800/month with 3 % inflation), the comparison is closer than this single number suggests. Real-world windfall decisions are rarely “invest vs. spend” in the abstract; they are “invest vs. specific alternative use,” and the alternative usually has its own compounding logic. Run both legs.

How to reproduce these

Each scenario above can be entered into the calculator using the inputs listed. The figures are rounded to the nearest hundred for narrative clarity; the calculator itself reports two-decimal precision. If you want to compare scenarios side by side, run them one at a time and screenshot the schedule, or copy the year-end balances into a spreadsheet.