SOLUTION: While she was travelling, Zainab 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.

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Question 1196613: While she was travelling, Zainab 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 $125 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 It turns out that interest is compounded daily on cash withdrawals, from the day the cash is withdrawn.
If the interest rate on cash withdrawals is 28%, what was her total bill when she got home?
What would be the total interest paid?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let A be the amount she withdrew each day: A+=+125

Let r be the daily growth factor based on the (annual) interest rate of 28%: r+=+1%2B.28%2F365

By the time she returns home...

the balance from her withdrawal on day 1 was Ar%5E20
the balance from her withdrawal on day 2 was Ar%5E19
...
the balance from her withdrawal on day 19 was Ar%5E2
the balance from her withdrawal on day 20 was Ar%5E1
the balance from her withdrawal on day 21 was Ar%5E0

Those daily balances form a geometric sequence; the sum of the balances is

A%28%281%2Br%29%5E21-1%29%2F%281%2Br%29%29

Use a calculator with the values of A and r to find the balance is $2645.24.

This answer can also be confirmed using a spreadsheet. Start with $125, multiply by the daily growth factor, add another $125, multiply again by the daily growth factor; and repeat for 21 days (but don't apply the growth factor on the last day).

The total amount of her withdrawals was 21($125) = $2625, so the amount of interest she paid was $20.24.

ANSWERS: balance $2645.24; interest $20.24

Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

The formula in the post by @greenestamps needs to be corrected.

The correct formula is

        the sum of daily balances is   A%2A%28%28r%5E21-1%29%2F%28r-1%29%29

with  "r"  defined as   1+%2B+0.28%2F365.