Extra $300 a month on a $400k mortgage: an AI's maths, checked

Your own answer

By adding $300 to your monthly payments from the start, you will save approximately $148,713 in total interest. Instead of taking 30 years to pay off the mortgage, you will pay it off in about 22.4 years (269 months), meaning you finish paying 7.6 years earlier.

Claim by claim

• "M ≈ $2,530.30" Wrong. The AI made a calculation error on the standard monthly principal and interest payment. The correct standard payment for a $400,000 mortgage at 6.5% for 30 years is $2,528.27.

• "N ≈ 294 months" Wrong. The AI hallucinated the result of its own logarithm equation. Using the correct new payment of $2,828.27, the math results in 268.9 months, meaning the loan is paid off in 269 months (not 294).

• "30.0 - 24.5 ≈ 5.5 years earlier" Wrong. Because the payoff time is 269 months (approx 22.4 years), the mortgage is paid off 7.6 years earlier, not 5.5 years earlier.

• "510,900 - 432,000 ≈ 78,900" Wrong. Because the AI calculated the loan term incorrectly, its interest calculations are off by a massive margin. The correct interest saved is $148,713.

What it missed

The AI calculated the total paid with the extra amount by blindly multiplying the rounded months by the payment ($294\times 2,830.30$). In reality, the final payment on an amortized loan is almost always a partial payment to clear the exact remaining balance. In this scenario, you make 268 full payments of $2,828.27, and one final partial payment of about $3,487.50 to clear the last bit of principal and interest.

Corrected answer

Let:

• Principal $P=400,000$
• Term $=30$ years $\Rightarrow 360$ monthly payments
• APR $=6.5\%$ so monthly rate $r=0.065/12$
• Required payment (no extra) would be $M$
• With extra payment $=300$, new payment is $M+300$

1) Monthly payment on the original mortgage

This comes out to approximately:

With the extra:

2) Payoff time with the extra $300/month

Payoff time $N$ in months satisfies:

Solving for $N$ gives approximately:

So the payoff is about:

3) Interest saved

Total interest saved = (interest without extra) − (interest with extra).

• Without extra: total paid

Interest:

• With extra: total paid

Interest:

Difference (interest saved):

Results (rounded)

• Interest saved: about $148,700
• Payoff earlier: about 7.6 years (paid off around 22.4 years instead of 30)

If you want, I can redo this using your lender’s exact rounding/payment calculation method (many lenders slightly adjust the amortization due to rounding).

Your own answer

I get a base payment of about $2,528.27. Adding $300 makes it $2,828.27, and the loan is then paid off in about 269 months (roughly 22 years 5 months). That is about 7.5 years early and saves about $150,000 in interest. The other AI's final figures (5.5 years, $79,000) are far too low.

Claim by claim

• Setup (P = 400,000, 360 payments, r = 0.065/12, extra applied to the payment): holds.
• "M ≈ $2,530.30": slightly wrong. The correct payment is about $2,528.27. The error is only about $2 a month, but it carries into the later figures.
• "N ≈ 294 months": wrong. Using N = −ln(1 − P·r/payment) / ln(1+r):
  • P·r = 2,166.67, and dividing by 2,828.27 gives 0.7661.
  • ln(1 − 0.7661) ≈ −1.4528, and ln(1+r) ≈ 0.005402.
  • N ≈ 268.9, so about 269 months, or about 22.4 years.
  • 294 months is not close to this.
• "30.0 − 24.5 ≈ 5.5 years earlier": wrong. The arithmetic follows from the bad N, but the correct result is about 7.5 years earlier (91 months, or 7 years 7 months).
• "360 · 2,530.30 ≈ 910,908" and interest of about $510,908: nearly right. With the correct payment, 360 × 2,528.27 ≈ $910,177, so interest is about $510,200. The error is small.
• "294 · 2,830.30 ≈ 832,? (about) ≈ 832,000" and interest of about $432,000: wrong. This depends on the bad N. The correct total paid is about 268.9 × 2,828.27 ≈ $760,600, so interest is about $360,600. The "832,?" in the working also looks unfinished.
• "Interest saved: about $79,000": wrong. The correct figure is about $510,200 − $360,600 ≈ $149,500, nearly double.

What it missed

• It didn't check its result for plausibility. $300 extra on a $400k loan at 6.5% cuts the term by more than 5.5 years, because the extra goes straight to principal early, when most of each payment is interest.
• It didn't mention that the final payment is partial, which is why N isn't a whole number.
• The offer to "redo using your lender's exact rounding" is a distraction. Rounding changes the result by a few dollars, not tens of thousands.

Corrected answer

• Base payment: about $2,528.27 a month, with total interest of about $510,200 over 30 years.
• With $300 extra (a $2,828.27 total payment): the loan is paid off in about 269 months (about 22 years 5 months).
• Time saved: about 7.5 years (about 91 months).
• Interest paid: about $360,600.
• Interest saved: about $149,500, or roughly $150,000.