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 It turns out that interest is compounded daily on cash withdrawals, beginning from the moment the cash is withdrawn.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?

To calculate Zaina's total bill when she got home, we need to consider the interest charged on her daily cash withdrawals.

Step 1: Calculate the total amount withdrawn
Zaina withdrew $200 every day for 21 days.
Total amount withdrawn = $200 x 21 = $4200

Step 2: Calculate the interest charged on cash withdrawals
The interest rate on cash withdrawals is 28%.

To calculate the interest compounded daily, we use the formula:

Total Amount = Principal Amount x (1 + Interest Rate)^Number of Periods

In this case, the Principal Amount is $4200, the Interest Rate is 28%, and the Number of Periods is 21.

Total Amount = $4200 x (1 + 28%)^21

Step 3: Calculate the total bill when she got home
The total bill when she got home is the sum of the amount withdrawn and the interest charged on the cash withdrawals.

Total bill = Total amount withdrawn + Total interest charged

Total bill = $4200 + (Total Amount - Principal Amount)

Total bill = $4200 + ($4200 x (1 + 28%)^21 - $4200)

By calculating the above equation, the total bill when Zaina got home can be determined.

To calculate Zaina's total bill upon returning home, we need to consider the cash withdrawals, interest rate, and the compounding period.

First, we need to calculate the total amount Zaina withdrew over 21 days. Since she withdrew $200 every day, we can multiply $200 by 21 to get $4,200.

Next, we need to calculate the total interest charged. Since the interest is compounded daily, we need to calculate the interest for each day and sum them up.

To calculate the interest for a single day, we can use the formula:
Interest for the day = (Principal amount) x (Daily interest rate)
Where the principal amount is the total withdrawn for the day (which is $200) and the daily interest rate is the annual interest rate divided by 365.

Let's calculate the interest for the entire period:

1. Calculate the daily interest rate: 28% / 365 = 0.0767% (approx.)

2. Multiply the principal amount by the daily interest rate for each day and sum them up for 21 days:

Day 1: $200 x 0.0767% = $0.1534 (approx.)
Day 2: $200 x 0.0767% = $0.1534 (approx.)
...
Day 21: $200 x 0.0767% = $0.1534 (approx.)

Total interest = ($0.1534) x 21 = $3.22014 (approx.)

Finally, we calculate the total bill by adding the withdrawn amount and the interest charged:
Total bill = Withdrawn amount + Total interest
Total bill = $4,200 + $3.22014 = $4,203.22 (approx.)

Therefore, when Zaina got home, her total bill was approximately $4,203.22.

so, look at the amounts, including daily interest. The 1st day's $200 was charged interest 21 times, the 2nd day's 20 times, etc. This adds up to

200(1+r)^21 + 200(1+r)^20 + ... + 200(1+r)^1

where r = 0.28/365

This is just a GP with the last term (200) excluded, where
a = 200
r = (1+0.28/365)

You want S21-200

Just plug your numbers into the GP sum formula which you know.