Final answer:
Simon will take approximately 53 months to pay off the card with the minimum monthly payment of $10. With a monthly payment of $30, it will take him approximately 19 months. Simon will make $40 more in total payments under the $10-a-month plan than under the $30-a-month plan.
Step-by-step explanation:
a. If Simon makes the minimum monthly payment of $10, it will take him approximately 53 months to pay off the card.
To calculate this, we can use the formula for the number of months required to pay off a credit card balance:
Number of months = (log(A/P))/(log(1+i))
Where A is the initial balance, P is the monthly payment, and i is the monthly interest rate expressed as a decimal.
Using the given values, we have:
Number of months = (log(350/10))/(log(1+0.18/12))
= (log(35))/(log(1.015))
= 53 (rounded to the nearest month).
b. If Simon makes a monthly payment of $30, it will take him approximately 19 months to pay off the card.
Using the same formula:
Number of months = (log(350/30))/(log(1+0.18/12))
= (log(11.67))/(log(1.015))
= 19 (rounded to the nearest month).
c. The total payments will be calculated by multiplying the monthly payment by the number of months it takes to pay off the card under each plan.
Under the $10-a-month plan:
Total payments = $10 x 53 = $530
Under the $30-a-month plan:
Total payments = $30 x 19 = $570
Hence, Simon will make $40 more in total payments under the $10-a-month plan than under the $30-a-month plan.