The 15-Year Versus 30-Year Arithmetic
The worked example that follows uses specific interest-rate, return, and balance assumptions — 4% on the 30-year, 3% on the 15-year, 7% on the investment portfolio — as an illustration of how strategic-debt arithmetic plays out. The rates were typical of the 2015–2021 window; re-run the comparison with your actual quoted rate. Be clear about what the 7%-versus-4% gap is: an equity risk premium you are choosing to collect with borrowed money, not a free spread. The correct hurdle for a prepayment is a risk-matched bond yield, not your portfolio’s expected return (section “Prepay or Invest? Compare the Right Two Things”); the example uses equities because that is what people actually do with the difference, and because the conclusion that survives the rate change is about liquidity, not return. Plug in your own numbers before deciding.
Let’s dive into an example with Sam, who’s in a similar situation to Alex. Sam earns $75,000 annually, aims to purchase a $500,000 home, and has saved $300,000 (60%) for the down payment. This leaves Sam needing a $200,000 mortgage. Faced with the choice between a 30-year fixed mortgage at 4% and a 15-year fixed mortgage at 3%, Sam, who prefers to be debt-free as soon as possible, opts for the 15-year option at 3%. This decision results in a monthly mortgage payment of $1,381, with 36% of that first payment going towards interest.
Alex is keen on growing their wealth and is comfortable taking on a reasonable amount of debt to achieve this. They opt for a 30-year mortgage at 4%, resulting in a monthly payment of $955, with nearly 70% of the first payment being interest. This strategy allows Alex to save $426 monthly compared to Sam, who chooses a different path. Alex invests this $426 into a stock index fund with an average annual return of 7%. Fifteen years later, Sam owns their home outright, but still has ongoing costs like property taxes and maintenance. Alex, on the other hand, still owes over $129,000 on their mortgage but has amassed over $135,000 in investments, enough to pay off the mortgage and have $6,000 to spare. At first glance, the extra $6,000 might not seem significant. After 15 years, Alex has chipped away only about $70,000 of the principal — the bulk of their payments went to interest. This frustrates many, feeling like they’ve “wasted” money on interest, which is why there’s often a rush to pay off mortgages.
However, Alex’s situation is more advantageous. While Sam’s $200,000 is tied up in their home, Alex has $135,000 in liquid assets. To access their home equity, Sam’s options are limited to either opting for a cash-out refinancing, which they’re hesitant to do, or selling their home. However, selling would require finding a new place to live, potentially at an equal or higher cost. Moreover, Alex has a 15-year head start in investing, which significantly impacts their financial growth over time.
Run the clock to year 30 and the gap is explicit. Both computations below are the annuity future-value formula of section “Loan Amortization (Annuities)”, , with a monthly rate and the number of monthly contributions as . Sam, mortgage-free at year 15, redirects the full $1,381 into the index fund for the remaining fifteen years ():
Alex, who declines to prepay and simply keeps investing $426 a month for the whole thirty years while the 30-year note amortizes on schedule:
After 30 years both own their homes free and clear, but Alex is ahead by roughly $82,000 — on a strategy that also left them liquid the entire time. The whole edge comes from the spread: 7% compounding against a 4% loan for three decades, with the small monthly difference given the longest possible runway.
Now re-run it at 2026 rates and watch the edge disappear. At 6.5% on the 30-year and 5.75% on the 15-year, the payments are $1,264 and $1,661 and the monthly difference is $397. Alex’s fund at year 15 holds $125,700 against a remaining balance of $145,100: Alex cannot pay off the house when Sam does. At year 30 Sam’s redirected $1,661 has grown to $526,400 and Alex’s $397 to $483,900. Sam wins by $42,000, and by $75,000 if the quotes are 7% and 6.25%. Alex’s fund would need to return 7.75% a year, every year, just to tie. The return argument for the longer loan is a low-rate artifact, and the same arithmetic run against a bond yield instead of 7% equities loses in every regime — which is the point of section “Prepay or Invest? Compare the Right Two Things”.
What does survive is the option. In the low-rate version Alex could have paid off the 30-year mortgage at year 15 — the fund had surpassed the balance — and chose not to; what they bought was financial flexibility, optionality that outranks the marginal dollar of accumulated wealth. At 2026 rates the option costs money instead of paying for itself, so you are buying liquidity rather than getting it free. The next section prices what that liquidity is worth.