How To Pay Off Debt Calculator

The formula this calculator uses

months = -ln(1 - r x balance / payment) / ln(1 + r)

B

The balance outstanding at the start

r

Monthly interest rate, the annual rate divided by twelve

P

The fixed payment made every month

n

Number of payments needed to clear the balance

How to check the result by hand

1. 1

   Convert the annual rate to a monthly one

   Divide the annual percentage rate by twelve. On 18% the monthly rate is 1.5%, and that figure is what each month's interest is charged on.

2. 2

   Check the payment covers the interest

   Multiply the balance by the monthly rate. If the payment does not exceed that figure the balance grows rather than shrinks, and no schedule will clear it.

3. 3

   Solve for the number of payments

   Apply the logarithmic formula. A £5,000 balance at 18% with £250 a month gives roughly 24 payments, well beyond the 20 a zero-interest division suggests.

4. 4

   Multiply out to find the total paid

   Payment times number of payments gives everything paid. Subtracting the original balance leaves the total interest, which is the cost of the schedule.

5. 5

   Repeat with the extra payment

   Add an extra payment and solve again. The new schedule is shorter, and the interest saved is the difference between the two totals rather than the extra payments themselves.