Finance⏱ 5 min read
How to Calculate Exactly When Your Debt Will Be Paid Off
Knowing your payoff date transforms debt repayment from abstract to concrete. Here is the formula for any fixed monthly payment, how extra payments affect the timeline, and the avalanche vs snowball comparison.
Most people making minimum payments on debt have no idea when -- or whether -- they will ever pay it off. The maths is not complicated, and seeing the numbers clearly is the first step to paying debt off faster.
The Payoff Time Formula
n = -log(1 - (r x B) / P) / log(1 + r)
n = number of monthly payments to pay off
r = monthly interest rate (annual rate / 12)
B = current balance
P = fixed monthly payment
Example: £8,000 credit card, 21% APR, paying £250/month
r = 21% / 12 = 1.75% per month = 0.0175
n = -log(1 - (0.0175 x 8,000) / 250) / log(1.0175)
= -log(1 - 0.56) / log(1.0175)
= -log(0.44) / 0.01735
= -(-0.8210) / 0.01735
= 47.3 months = just under 4 years
Total paid: 47 x £250 + final payment = approximately £11,750-£11,900
Total interest: approximately £3,750-£3,900
Minimum Payment Trap
Most credit cards charge minimum payment of:
2-3% of balance, or £25, whichever is greater
£8,000 balance, 21% APR, minimum payment (2%):
Starting minimum: £8,000 x 2% = £160/month
Payoff time: approximately 34-35 YEARS
Total interest: approximately £7,400+
Same balance at £250/month fixed: 47 months, ~£3,800 interest
Same balance at £400/month fixed: 25 months, ~£2,000 interest
The minimum payment is designed to keep you paying for decades.
Even a modest increase in payment has dramatic impact on payoff time.
Extra Lump Sum Payments
Impact of a £500 extra payment on the £8,000 balance example:
(£250/month, 21% APR)
Without extra payment: 47 months, ~£3,800 interest
With £500 extra in month 1: new balance £7,500
n = -log(1-(0.0175x7,500)/250) / log(1.0175) = 42.4 months
Saving: 4-5 months and approximately £1,100 in interest
Rule of thumb: each £100 of extra principal payment early
saves approximately 5x in future interest on a high-rate debt
(at 20%+ APR, early repayment is the best investment available)
Debt Avalanche vs Debt Snowball Comparison
Three debts:
Debt A: £3,000 at 28% APR
Debt B: £6,000 at 18% APR
Debt C: £1,500 at 12% APR
Total: £10,500, extra payment budget £300/month above minimums
Avalanche (highest rate first -- A, then B, then C):
Total interest paid: approximately £3,400
Payoff time: approximately 38 months
Snowball (lowest balance first -- C, then A, then B):
Total interest paid: approximately £4,100
Payoff time: approximately 40 months
Avalanche saves ~£700 and 2 months.
Snowball provides earlier wins (debt C gone in 5 months).
Mathematical winner: always avalanche.
Behavioural winner: whichever method you will actually stick to.