Answer: The credit card balance of $941.14 is decreasing by $20 per month, but it's also increasing due to the annual interest rate of 13.99% (or about 1.166% monthly when divided by 12). So the monthly interest will cause the balance to increase before the $20 payment is subtracted.
We can calculate the number of months it will take to pay off the unpaid balance using a formula for the number of periods to reach a certain future value with an ordinary annuity:
n = log[(PMT - PVr) / (PMT + FVr)] / log(1 + r)
where:
n is the number of months,
PMT is the monthly payment ($20),
PV is the present value ($0 in this case, as we are not considering any initial investment apart from the credit card debt),
r is the monthly interest rate (13.99%/12 = 1.166%/100 = 0.01166),
FV is the future value, which is the negative of the unpaid balance (-$941.14, as we are calculating the time until the debt is paid off).
Substituting the known values into the formula:
n = log[(20 - 0*0.01166) / (20 + (-941.14)*0.01166)] / log(1 + 0.01166)
Now, we can compute the result. Keep in mind that the logarithm function (log) is the natural logarithm.
After performing the calculation and rounding up to the nearest whole number (since we can't have a fraction of a month), we find the number of months it will take to pay off the unpaid balance.
NOTE: This is an approximation method and doesn't account for minimum balance requirements or additional fees that might be charged by the credit card company. The actual number of months might be slightly more due to these factors. Please consult with a financial advisor or use a dedicated credit card payoff calculator for more accurate results.