Debt Payoff vs Invest: Which Wins With Extra Cash?

How the comparison works

On the defaults — $300.00 a month extra, a $5,000.00 debt at 22.00% APR and an 8.00% investment return — the debt is gone in 20.07 months, the pay route costs $6,021.42 in total and $1,021.42 of that is interest, while investing the same $300.00 a month grows to $6,420.03 and the untouched debt grows to $7,200.00, so the invest route ends $779.97 behind — PAY THE DEBT wins by $779.97.

Both routes spend the same total cash — $300 a month for 20.07 months — the comparison is net wealth at month 20.07, not cash spent. In the invest route the debt is left untouched: no minimum payments are modelled, and real minimum payments shrink the gap, because they slow the debt’s growth. The horizon is the payoff time, about 20.1 months at the defaults — not a round number of years, because the months come from the payoff formula, not from a calendar choice.

Paying the debt is a GUARANTEED return equal to the APR, while the investment return is only an average — that is why the debt usually wins until the return beats the APR. The invest route only pulls ahead when the return tops the APR: at a 25.00% return it wins by $182.05, and it needs 22.00% just to tie. Taxes are NOT included — the investment gains would be taxed, which would widen the pay route’s lead.

The worked example, line by line

Setup: $300.00 a month extra, $5,000.00 debt, 22.00% APR, 8.00% investment return.

Line 1 — the monthly rates. Monthly debt rate = 22.00% ÷ 12 = 1.8333% a month; monthly invest rate = 8.00% ÷ 12 = 0.6667% a month. The monthly interest on $5,000.00 is $91.67 — the $300.00 payment covers it with room to spare, so the debt shrinks.

Line 2 — the months to debt-free. n = −ln(1 − 5000 × 0.018333 ÷ 300) ÷ ln(1.018333) = 20.07 months — fractional months, not whole ones: the last payment is smaller than $300.00.

Line 3 — the total paid and the interest. $300.00 × 20.07 = $6,021.42 total paid; interest = $6,021.42 − $5,000.00 = $1,021.42.

Line 4 — the invest route. $300.00 × ((1.006667)^20.07 − 1) ÷ 0.006667 = $6,420.03 after 20.07 months of $300.00 deposits.

Line 5 — the debt untouched, the net, and the gap. $5,000.00 × (1.018333)^20.07 = $7,200.00; net = $6,420.03 − $7,200.00 = −$779.97; gap = $779.97 — PAY THE DEBT wins by $779.97. The default result in full: Months to debt-free 20.07, total interest $1,021.42, invest route $6,420.03 vs debt $7,200.00, net -$779.97 — PAY THE DEBT wins by $779.97.

Line 6 — the rounding convention. Rounding convention: every gap on this page is the difference of the displayed totals: each side is rounded to cents first, then subtracted. On these defaults the unrounded net and the displayed net agree at −$779.97, but on other inputs they can differ by a cent, and the page always shows the displayed figure.

Every branch, checked

Extra $500/mo: 11.15 months, interest $573.87, invest route $5,766.29 vs debt $6,122.45, net −$356.16 — PAY THE DEBT wins by $356.16. More cash shortens the horizon to 11.15 months, and a shorter horizon leaves less time for the investment to compound — the gap shrinks, but the debt still wins.

Extra $100/mo: 136.78 months, interest $8,677.91, invest route $22,221.42 vs debt $60,000.00, net −$37,778.58 — PAY THE DEBT wins by $37,778.58. At $100 a month the debt takes over 11 years to clear, and the untouched balance balloons to $60,000.00 — the longer the debt runs, the worse the invest route looks.

Debt APR 10%: 18.02 months, interest $405.54, invest route $5,723.38 vs debt $5,806.45, net −$83.07 — PAY THE DEBT wins by $83.07. A cheaper debt nearly ties — at 10.00% APR the gap is only $83.07, and at 8.00% it is exactly $0.00.

Invest return 12%: 20.07 months, interest $1,021.42, invest route $6,631.71 vs debt $7,200.00, net −$568.29 — PAY THE DEBT wins by $568.29. Even a 12.00% return cannot beat a 22.00% APR over 20 months — the return has to beat the APR, not just look big.

Invest return 25%: 20.07 months, interest $1,021.42, invest route $7,382.05 vs debt $7,200.00, net +$182.05 — INVEST wins by $182.05. The return finally beats the APR, and the investment pulls ahead — but only by $182.05, and only on an average return that is not guaranteed.

Balance $10,000: 51.99 months, interest $5,596.07, invest route $18,566.82 vs debt $25,714.29, net −$7,147.47 — PAY THE DEBT wins by $7,147.47. Doubling the balance more than doubles the horizon to 51.99 months, and the gap explodes — big debts punish the invest route hardest.

The reverses, worked backwards

Investment return for a TIE: exact 22.0000%; displayed 22.00% → invest route $7,200.00, debt $7,200.00, net $0.00, TIE. At 22.00%: Months to debt-free 20.07, total interest $1,021.42, invest route $7,200.00 vs debt $7,200.00, net $0.00 — TIE. At 21.99%: Months to debt-free 20.07, total interest $1,021.42, invest route $7,199.40 vs debt $7,200.00, net -$0.60 — PAY THE DEBT wins by $0.60. This tie is EXACT by construction — the break-even invest return equals the debt APR (22.00%). The star is a PERCENT. This reverse is CONTINUOUS.

Debt APR for a TIE: exact 8.0000%; displayed 8.00% → invest route $5,625.00, debt $5,625.00, net $0.00, TIE. At 8.00%: Months to debt-free 17.73, total interest $317.88, invest route $5,625.00 vs debt $5,625.00, net $0.00 — TIE. At 7.99%: Months to debt-free 17.72, total interest $317.46, invest route $5,624.52 vs debt $5,624.12, net $0.40 — INVEST wins by $0.40. This tie is EXACT by construction — the break-even debt APR equals the invest return (8.00%). The star is a PERCENT. This reverse is CONTINUOUS.

Extra $/month to pay off in 12 months: exact $467.9719; displayed $467.97 → 12.0001 months. At $467.97: Months to debt-free 12.00, total interest $615.67, invest route $5,826.22 vs debt $6,217.99, net -$391.77 — PAY THE DEBT wins by $391.77. One cent less, $467.96: Months to debt-free 12.00, total interest $615.68, invest route $5,826.24 vs debt $6,218.02, net -$391.78 — PAY THE DEBT wins by $391.78 — the payoff takes 12.0003 months, and one cent less rounds to the same 12.00 months — this reverse is exact, not a step. The star is DOLLARS/MONTH. This reverse is CONTINUOUS.

Debt balance paid off in 24 months: exact $5782.7809; displayed $5,782.78 → 24.0000 months. At $5,782.78: Months to debt-free 24.00, total interest $1,417.22, invest route $7,779.96 vs debt $8,943.26, net -$1,163.30 — PAY THE DEBT wins by $1,163.30. $1 less, $5,781.78: Months to debt-free 23.99, total interest $1,416.66, invest route $7,778.13 vs debt $8,940.86, net -$1,162.73 — PAY THE DEBT wins by $1,162.73 — the payoff takes 23.9948 months — 23.99 at the displayed two decimals, a hundredth under 24.00; this reverse is exact, not a step. The star is DOLLARS. This reverse is CONTINUOUS.

Investment return to be ahead by $1,000: exact 37.4505%; displayed 37.45% → net +$999.97. At 37.45%: Months to debt-free 20.07, total interest $1,021.42, invest route $8,199.97 vs debt $7,200.00, net $999.97 — INVEST wins by $999.97. At 37.44%: Months to debt-free 20.07, total interest $1,021.42, invest route $8,199.27 vs debt $7,200.00, net $999.27 — INVEST wins by $999.27. The star is a PERCENT. This reverse is CONTINUOUS.

Extra $/month to pay off in 6 months: exact $887.6149; displayed $887.61 → 6.0000 months. At $887.61: Months to debt-free 6.00, total interest $325.69, invest route $5,415.25 vs debt $5,575.84, net -$160.59 — PAY THE DEBT wins by $160.59. One cent less, $887.60: Months to debt-free 6.00, total interest $325.69, invest route $5,415.25 vs debt $5,575.84, net -$160.59 — PAY THE DEBT wins by $160.59 — the payoff takes 6.0001 months, and one cent less rounds to the same 6.00 months — this reverse is exact, not a step. The star is DOLLARS/MONTH. This reverse is CONTINUOUS.

What the defaults assume

Both routes spend the same total cash — $300 a month for 20.07 months — the comparison is net wealth at month 20.07, not cash spent. In the invest route the debt is left untouched: no minimum payments are modelled, and real minimum payments shrink the gap, because they slow the debt’s growth. Paying the debt is a GUARANTEED return equal to the APR, while the investment return is only an average. Taxes are NOT included — the investment gains would be taxed, which would widen the pay route’s lead. With only $50.00 a month extra (The debt never pays off — the $50.00 payment is below the $91.67 monthly interest.) the debt NEVER pays off — the balance grows by $41.67 in month 1, because the payment is below the $91.67 monthly interest: a model-level outcome, not an error. With $5,000.00 a month extra (Months to debt-free 1.02, total interest $92.52, invest route $5,092.83 vs debt $5,093.38, net -$0.55 — PAY THE DEBT wins by $0.55) the debt is gone in 1.02 months and the two routes are nearly tied — at a one-month horizon there is almost no time for either side to grow. With a 0.00% debt APR (Months to debt-free 16.67, total interest $0.00, invest route $5,269.82 vs debt $5,000.00, net $269.82 — INVEST wins by $269.82) the debt costs nothing to carry, so investing wins by $269.82. With a 0.00% investment return (Months to debt-free 20.07, total interest $1,021.42, invest route $6,021.42 vs debt $7,200.00, net -$1,178.58 — PAY THE DEBT wins by $1,178.58) the invest route is just the cash sitting still, and it loses by $1,178.58. With a $0.00 balance (Months to debt-free 0.00, total interest $0.00, invest route $0.00 vs debt $0.00, net $0.00 — TIE) there is no debt and nothing to compare — a TIE, and a model-level outcome, not an error. Rounding convention: every gap on this page is the difference of the displayed totals: each side is rounded to cents first, then subtracted.

Output · formula · meaning

Who uses this

• The cardholder with a $5,000.00 balance at 22.00% APR: they learn paying it off with $300.00 a month leaves them $779.97 ahead of investing the same cash — and they check the $500.00-a-month branch, where the gap shrinks to $356.16.
• The saver with $100.00 a month to spare: they learn that at $100.00 a month the debt takes 136.78 months and the invest route falls $37,778.58 behind — and they check the never-state edge, where $50.00 a month never pays the debt off at all.
• The investor earning 12.00% while carrying 22.00% debt: they learn the investment still loses by $568.29 — and they check the tie reverse, where the return must reach 22.00% just to break even.
• The borrower deciding how fast to pay: they learn $467.97 a month clears the debt in exactly 12 months — and they check the 6-month reverse, where $887.61 a month does it in 6.0000 months.

Accuracy & limitations

The math is first-principles, closed form: months to debt-free n = −ln(1 − B·rm/P) ÷ ln(1+rm) with fractional months, total paid = P × n, total interest = P × n − B, invest route FV = P × ((1+im)^n − 1)/im, debt if untouched = B × (1+rm)^n, and the gap is the difference of the displayed totals — each side rounded to cents first, then subtracted. Every figure is rounded to cents half-up. What the model cannot do is predict YOUR rates and returns: the investment return is an average, not a guarantee — a 25.00% average that arrives as a few great years and a few bad ones behaves differently from a steady 25.00%, and the debt’s 22.00% APR is charged every month without fail. No minimum payments are modelled — real minimum payments shrink the gap, because they slow the debt’s growth. Taxes are NOT included — the investment gains would be taxed, which would widen the pay route’s lead — and no fees are modelled on either side. Use it to compare the two routes on the same numbers, then check the real APR, the real return history, and the tax treatment before you choose.

Frequently asked questions