Joy has 'no interest fee period' credit card that charges 12.25% p.a. interest. Her statement is dated the 26th day of month. In the month of July, Joy makes the following transactions on her credit card.
On:
5th of July, she purchased a wrist watch for K32.
12th of July, she took out a cash advance of K130.
22nd July, she did her groceries payment of K128.
According to the information calculate:
1. The number of days.
2. The total amount owing that will appear on her statement on 26th July.
1. The number of days between each transaction and the statement date of 26th July are as follows:
- 5th July to 26th July = 21 days
- 12th July to 26th July = 14 days
- 22nd July to 26th July = 4 days
2. To calculate the total amount owing on her statement on 26th July, we need to consider the following:
- Wrist watch purchase on 5th July: K32
- Cash advance on 12th July: K130 (Note: cash advances typically have higher interest rates and are usually charged interest from the day of the transaction)
- Groceries payment on 22nd July: K128
First, let's calculate the interest accrued on the cash advance:
K130 * 12.25% / 365 * 14 days = K0.74
So, the total amount owing on her statement on 26th July would be:
K32 (wrist watch) + K130 (cash advance) + K128 (groceries) + K0.74 (interest on cash advance) = K290.74
Therefore, Joy would owe a total of K290.74 on her credit card statement on 26th July.
Use this formula to calculate the days:
End date = 26
End date - Purchase date + 1
Using the formula provided to calculate the number of days:
1. Wrist watch purchase on 5th July:
End date - Purchase date + 1 = 26 - 5 + 1 = 22 days
2. Cash advance on 12th July:
End date - Purchase date + 1 = 26 - 12 + 1 = 15 days
3. Groceries payment on 22nd July:
End date - Purchase date + 1 = 26 - 22 + 1 = 5 days
Using this formula, we get the same number of days as calculated earlier.
Use those dates above to redo 2.
Using the calculated days for each transaction, let's recalculate the total amount owing on Joy's credit card statement on 26th July:
1. Wrist watch purchase on 5th July (22 days):
K32 + (K32 * 12.25% / 365 * 22) = K32 + K0.23 = K32.23
2. Cash advance on 12th July (15 days):
K130 + (K130 * 12.25% / 365 * 15) = K130 + K0.64 = K130.64
3. Groceries payment on 22nd July (5 days):
K128 + (K128 * 12.25% / 365 * 5) = K128 + K0.23 = K128.23
Total amount owing on her statement on 26th July:
K32.23 (wrist watch) + K130.64 (cash advance) + K128.23 (groceries) = K291.10
Therefore, Joy would owe a total of K291.10 on her credit card statement on 26th July.
Use this formula: A = P[1+(rT/100)] to calculate 2.
To calculate the total amount owing on Joy's credit card statement on 26th July using the formula A = P[1+(rT/100)]:
Where:
A = Total amount owing
P = Principal amount (original amount spent)
r = Annual interest rate
T = Time period in years (fraction of days/365)
1. Wrist watch purchase on 5th July (22 days):
Principal (P) = K32
Annual interest rate (r) = 12.25%
Time period (T) = 22/365
A1 = K32 *[1 + (12.25 * 22) / (100 * 365)]
A1 = K32 * [1 + 0.0739]
A1 = K32 * 1.0739
A1 = K34.44
2. Cash advance on 12th July (15 days):
P = K130
r = 12.25%
T = 15/365
A2 = K130 *[1 + (12.25 * 15) / (100 * 365)]
A2 = K130 * [1 + 0.0504]
A2 = K130 * 1.0504
A2 = K136.55
3. Groceries payment on 22nd July (5 days):
P = K128
r = 12.25%
T = 5/365
A3 = K128 *[1 + (12.25 * 5) / (100 * 365)]
A3 = K128 * [1 + 0.0206]
A3 = K128 * 1.0206
A3 = K130.94
Total amount owing on her statement on 26th July:
A = A1 + A2 + A3
A = K34.44 + K136.55 + K130.94
A = K301.93
Therefore, Joy would owe a total of K301.93 on her credit card statement on 26th July.