Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

please show all work. thanks! ewards for purchases you make with an option of tw

ID: 2885156 • Letter: P

Question

please show all work. thanks!
ewards for purchases you make with an option of two ways to redeem your have a lump sum deposited into unt, suppose that you know that based on how much you will use the credit card, the sm they would deposit would be $500. The second option is that you can have rewards 5. Suppose that you have a credit card that gives you cash r the card. Suppose that the credit card company gives you rewards. The first is that after a year of using the card, you cain lump continuously deposited into your bank account over the course of the know that based deposited continuously over the course of the year. Suppose that the bank ac e deposited into earns 5% take? Justify your answer. on how much you will use the card, the amount they will deposit will be $490, count that this will annual interest, compounded continuously. Which option should you

Explanation / Answer

THis problem is based on compound interest when the interest rate is compounded continuously.

In option one $ 500 are deposited at the end of the year in the bank account.

In the second option :

Amount deposited is, P = $ 490

and The bank account in which this is deposited earns an interest of = 5% per annum and this interses is
compounded continuously

And the time is , t = 1year


=> When the interses is continuously compounded we use

A = Pe^(rt)

where A is the amount after time 't'
P is the sum deposited
r is the annual interses rate compounded continuously
t is the time period

=> A = 490e^(5/100*1)

     = 490e^(0.05)

     = 515.123

Hence in option 2 the final amount that we would recieve is = $ 515.123. This is more than what we get in option 1.

Hence option 2 is the better option.