Question

amThe balance on a credit card, that charges a 10.5%APR interest rate, over a 1 month period is given inthe following table:Days 1-5: $200 (initial balance)Days 6-20: $350 ($150 purchase)Days 21-30: $150 ($200 payment)What is the finance charge, on the average dailybalance, for this card over this 1 month period?finance charge = $ [?]dredth

Answer 1

Solution:

The average daily balance is calculated below with the number of days given and the balance within that interval;

$\begin{gathered} =\frac{5(200)+15(350)+10(150)}{30} \\ =\frac{1000+5250+1500}{30} \\ =\frac{7750}{30} \\ =\text{ \ 258.33} \end{gathered}$

The annual percentage rate (APR) is given by 10.5%

Since 365 days are in a year, the daily percentage rate is given by;

$\begin{gathered} =\frac{10.5}{365} \\ =0.02876\text{ \%} \end{gathered}$

Hence, the daily finance charge on the average daily balance is;

$\begin{gathered} =\frac{0.02876}{100}\times258.33 \\ =\text{ \ 0.0743} \end{gathered}$

This daily finance charge over a period of one month (30days) will therefore be;

$\begin{gathered} =0.0743\times30 \\ =\text{ \ 2.229} \\ \\ To\text{ the nearest hundredth,} \\ =\text{ \ 2.23} \end{gathered}$

Therefore, the finance charge on the average daily balance for the credit card over 1 month period to the nearest hundredth is $2.23