Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% interest compounded co

Question

3 years ago

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Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% interest compounded co

ntinuously after that. Credit card B has an interest rate of 0.7%, also compounded continuously. If you are going to make a $500 dollar purchase and plan to not make a single payment for 2.5 years, which credit card would you go with? Explain for answer in 1-2 sentences.

Mathematics

2 answers:

motikmotik · Answer 1 · 2022-06-01T22:56:43+03:00

Answer:

Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.

Step-by-step explanation:

For credit card A the ammount will only be compounded after 1 year, so the total time elapsed for the laon is 1.5 years, while for the credit card B it'll be the full 2.5 years. To compute the total amount of a interest compounded continuously we must apply the formula:

M = C*e^(r*t)

Where M is the total amount, C is the initial amount, r is the interest rate and t is the time elapsed.

For credit card A:

M = 500*e^(0.008*1.5) = 506.03614

For credit card B:

M = 500*e^(0.007*2.5) = 508.8270

Since the total amount you have to pay for the purchase on the credit card A is lower, then it's the best option.