Question

While she was travelling, Zaina took advantage of the convenience of cash withdrawals on her credit card since her Canadian debit card wasn’t accepted in the country she was in. According to her travel budget she withdrew $200 every day for food, activities and shopping for 21 days.

When she got home, on the 21st day, she checked her credit card bill on-line and it showed that she had been charged interest already even though her payment wasn’t past due. It turns out that interest is compounded daily on cash withdrawals, beginning from the moment the cash is withdrawn. If the interest rate on cash withdrawals is 28%, what was her total bill when she got home?

Answer 1

@563blackghost

Answer 2

@Ultrilliam

Answer 3

@Elsa213

Answer 4

I think you would just have to get 28% of 200 and it to 200 then multiple by 21 for the days but I am not 100% sure

Answer 5

thank you!

Answer 6

I am not sure, you might wanna get what I said double checked though sorry

Answer 7

ok

Answer 8

Sarah, this is a geometric series

first of all, 28% per year is roughly equal to a daily rate of \(\dfrac{28}{365} \text{ %} \approx 7.7 \text { % } \).. Refine that if you like.

Day 21

She got back that day, so that $200 is just on her balance

Day 20

That day's $200 has been outstanding for 1 day and will be added to her balance as : \(200 (1 + 0.077)\), ie compounded for one day

Day 19

That day's $200 has been outstanding for 1 day and is added to her balance as : \(200 (1 + 0.077)^2\), ie compounded for two days

You get the idea

As there are 21 days worth of payments you have geometric series with 21 terms:

\( S = 200 + 200 (1 + 0.077) + 200 (1 + 0.077)^2 + \dots + 200 (1 + 0.077)^{\color{red}{20}}\)

\(= 200 ( 1 + (1 + 0.077) + (1 + 0.077)^2 + \dots + (1 + 0.077)^{20} )\)

Answer 9

take it from there?!

Answer 10

.....typo

Answer 11

thank you very much !!