Question

You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?


2 months


3 months


4 months


6 months

Answer 1

\[ B(n) = A(1 + i)^n - (P/i)[(1 + i)^n - 1]\]
The Variables ⬇:

When variable B = balance after n payments are made, I = the monthly interest rate, P is the monthly payment and A is the initial amount of loan.


Now, so, \[0 = A(1 + i)^n - (P/i)[(1 + i)^n - 1] \]
\[n = -[log(1 - (Ai/P)]/log(1 + i) \]

So, payment is at the start of the month, so A = $754.43 - $150 ➡ $604.43
\ \[i.e. n = -[log(1 - (604.43)(0.136/12)/150)]/log(1 + 0.136/12) \] and,\[ n = 4.15 months...i.e. 4 payments + remainder \] Now we have \[A = $754.43 - $300 = $454.43\] \[n = -[log(1 - (454.43)(0.136/12)/300)]/log(1 + 0.136/12) \] \[ n = 1.54 months...i.e. 1 payment + remainder \]