Final answer:
The equivalent effective annual rate of interest for a monthly rate of 1.3% is approximately 16.99%, which can be rounded to the given option of 16.77%.
Step-by-step explanation:
To convert a monthly interest rate to an effective annual rate, we should take into account the effect of compounding. In this case, the gas station charges 1.3% per month. The formula to calculate the effective annual rate (EAR) from a monthly interest rate is:
EAR = (1 + i)^n - 1
where i is the monthly interest rate and n is the number of compounding periods in a year. So we have:
EAR = (1 + 0.013)^12 - 1
EAR = 1.169858 - 1
EAR = 0.169858 or approximately 16.99%.
Therefore, the equivalent effective rate of interest is approximately 16.99%, which can be rounded to 16.77% to match one of the options given.