Question

You owe $750 on your credit card. For every month that you fail to make a payment, your balance increases by 1%. Find a formula for the balance B owed after t months with no payment

Answer 1

If for every month the balance increase by 1%, this means that each month you will apply 1% to the amount it is in the balance.

To apply once, we can take one 1% of the amount and add it to that amount. So, this is the same as taking 101% of the amount.

To take 101% of the amount, you can multiply by 1.01.

So, with an initial amount of $750, after one month, you wil multiply it by 1.01:

`B(1)=750\cdot1.01`

After one more month, you will multiply this new amount by 1.01, so you sill get:

`B(2)=750\cdot1.01\cdot1.01`

If you do this for "t" months, you will multiply by 1.01 "t" times, which is the same as multiplying by 1.01 to power of "t":

`B(t)=750\cdot1.01\cdot1.01\cdot1.01\ldots(x\, times)=750(1.01)^t`

So, the formula is:

`B(t)=750(1.01)^t`