yolandas credit card has an apr of 16.22% and a billing cycle of 30 days. the table below shows her…

yolandas credit card has an apr of 16.22% and a billing cycle of 30 days. the table below shows her transactions with that credit card in the month of november.\n| date | amount ($) | transaction |\n| ---- | ---- | ---- |\n| 11/1 | 857.14 | beginning balance |\n| 11/3 | 76.95 | purchase |\n| 11/10 | 50.00 | payment |\n| 11/24 | 43.19 | purchase |\nfind yolandas finance charge in november using the previous balance method, the adjusted balance method, and the daily balance method. among those three possible finance charges, what is the value of the one which is neither lowest nor highest?\n a. $12.53\n b. $11.59\n c. $12.05\n d. $10.91

yolandas credit card has an apr of 16.22% and a billing cycle of 30 days. the table below shows her transactions with that credit card in the month of november.\n| date | amount ($) | transaction |\n| ---- | ---- | ---- |\n| 11/1 | 857.14 | beginning balance |\n| 11/3 | 76.95 | purchase |\n| 11/10 | 50.00 | payment |\n| 11/24 | 43.19 | purchase |\nfind yolandas finance charge in november using the previous balance method, the adjusted balance method, and the daily balance method. among those three possible finance charges, what is the value of the one which is neither lowest nor highest?\n a. $12.53\n b. $11.59\n c. $12.05\n d. $10.91

Answer

Answer:

C. $12.05

Explanation:

Step1: Calculate finance - charge using previous - balance method

The previous - balance method uses the beginning balance to calculate the finance charge. The monthly interest rate $r=\frac{16.22%}{12}=\frac{0.1622}{12}$. The beginning balance $B = 857.14$. Finance charge $FC_1=B\times r=857.14\times\frac{0.1622}{12}\approx11.59$.

Step2: Calculate finance - charge using adjusted - balance method

The adjusted balance is the beginning balance plus purchases minus payments. Purchases $P = 76.95 + 43.19=120.14$, payment $M = 50.00$. Adjusted balance $B_{adj}=857.14 + 120.14-50.00 = 927.28$. Finance charge $FC_2=B_{adj}\times r=927.28\times\frac{0.1622}{12}\approx12.53$.

Step3: Calculate finance - charge using daily - balance method

  1. Calculate the number of days for each balance:
    • From 11/1 - 11/2: 2 days, balance $B_1 = 857.14$.
    • From 11/3 - 11/9: 7 days, balance $B_2=857.14 + 76.95=934.09$.
    • From 11/10 - 11/23: 14 days, balance $B_3=934.09 - 50.00 = 884.09$.
    • From 11/24 - 11/30: 7 days, balance $B_4=884.09+43.19 = 927.28$.
  2. Calculate the daily - balance:
    • $DB=\frac{(B_1\times2)+(B_2\times7)+(B_3\times14)+(B_4\times7)}{30}$
    • $DB=\frac{(857.14\times2)+(934.09\times7)+(884.09\times14)+(927.28\times7)}{30}$
    • $DB=\frac{1714.28+6538.63+12377.26+6490.96}{30}=\frac{27121.13}{30}\approx904.04$.
  3. Calculate the finance charge:
    • $FC_3=DB\times r=904.04\times\frac{0.1622}{12}\approx12.05$.
  4. Compare the three finance charges:
    • $FC_1\approx11.59$, $FC_2\approx12.53$, $FC_3\approx12.05$. The value that is neither the lowest nor the highest is $12.05$.