this table can be used to organize gigis credit card balances and payments over 6 months. the annual…

this table can be used to organize gigis credit card balances and payments over 6 months. the annual percentage rate on the credit card is 14%. what is the amount of interest charged for the first 6 months?\nmonth 1 2 3 4 5 6\nbalance $650 $354.08 $307.63 $260.64 $213.10 $165\npayment $300 $50 $50 $50 $50 $50\ninterest rate 0.01167 0.01167 0.01167 0.01167 0.01167 0.01167\ninterest charged $4.08

this table can be used to organize gigis credit card balances and payments over 6 months. the annual percentage rate on the credit card is 14%. what is the amount of interest charged for the first 6 months?\nmonth 1 2 3 4 5 6\nbalance $650 $354.08 $307.63 $260.64 $213.10 $165\npayment $300 $50 $50 $50 $50 $50\ninterest rate 0.01167 0.01167 0.01167 0.01167 0.01167 0.01167\ninterest charged $4.08

Answer

Explanation:

Step1: Identify monthly - interest rate

The annual percentage rate is 14%, so the monthly interest rate $r = \frac{14%}{12}\approx0.01167$.

Step2: Calculate interest for each month

For month 1: Interest $I_1=650\times0.01167 = 7.575$. For month 2: Balance $=650 - 300=350$, Interest $I_2 = 350\times0.01167=4.0845\approx4.08$. For month 3: Balance $=350 - 50 = 300$, Interest $I_3=300\times0.01167 = 3.501$. For month 4: Balance $=300 - 50=250$, Interest $I_4=250\times0.01167 = 2.9175$. For month 5: Balance $=250 - 50 = 200$, Interest $I_5=200\times0.01167=2.334$. For month 6: Balance $=200 - 50 = 150$, Interest $I_6=150\times0.01167 = 1.7505$.

Step3: Sum up the interests

$I=I_1 + I_2+I_3+I_4+I_5+I_6=7.575 + 4.08+3.501+2.9175+2.334+1.7505=22.158\approx22.16$.

Answer:

$$22.16$