# Business MathCalculate pay off debt with minimum payment only?

#### Juliayaho

##### New member
How can i calculate how many months it would take me to pay off a debt if I only make the minimum payment?

let say I ow 5000 my interest rate is 6.4% my payment rate is 2% so If i calculate my minimum payment I know it be 100 more or less but I i just pay that minimum how many month it would take me to pay off that debt and how much interest would I end up paying at the end?

what would be a formula to calculate that?
Thanks!!

#### Klaas van Aarsen

##### MHB Seeker
Staff member
How can i calculate how many months it would take me to pay off a debt if I only make the minimum payment?

let say I ow 5000 my interest rate is 6.4% my payment rate is 2% so If i calculate my minimum payment I know it be 100 more or less but I i just pay that minimum how many month it would take me to pay off that debt and how much interest would I end up paying at the end?

what would be a formula to calculate that?
Thanks!!
Hi Juliayaho!

I found this thread lying around.
Do you still want help on it?

If you pay 2% per period (is that per month?), it will take 50 periods.

The interest you pay is 6.4% over the original 5000, then 6.4% over the remaining 4900, and so on.
Btw, what is the period you pay 6.4% on? Is it a month? Or a year?
Assuming you pay 6.4% over the same period that make your payments of 2% for, the total interest you pay will be $6.4\% \times (5000 + 4900 + 4800 + ... + 100)$.

This is a so called arithmetic series.
Do you know how to calculate it?

#### Wilmer

##### In Memoriam
let say I ow 5000 my interest rate is 6.4% my payment rate is 2% so If i calculate my minimum payment I know it be 100 more or less but I i just pay that minimum how many month it would take me to pay off that debt and how much interest would I end up paying at the end?
You seem to be saying "if I pay 100 per month constantly":
quote: "I just pay that minimum"

If so, it will take approximately 58.3 months.

u = p / (p−ai)
v = 1 + i
n = LOG(u) / LOG(v)

n = number of payments(?)
p = monthly payment(100)
a = amount originally owing(5000)
i = interest monthly(.064/12)

u = 100/[100−5000(.064/12)]
v = 1+.064/12
n = LOG(u) / LOG(v) = 58.30898.....

Note that if instead you pay 2% of the opening month's balance,
then the initial \$100 payment will slowly reduce...
but theoretically you will never pay off!

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