natasha had a $922.93 balance on her credit card at the beginning of september. her credit card has an apr…

natasha had a $922.93 balance on her credit card at the beginning of september. her credit card has an apr of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. the following table shows natashas credit card purchases over the next two months.\n| month | cost ($) |\n| ---- | ---- |\n| september | 33.70 |\n| october | 61.70 |\n| october | 27.80 |\nif natasha makes only the minimum payments, what will her balance at the beginning of november? (assume that the interest accrues before the monthly payment, and that the monthly payment occurs at the end of the month. round all dollar values to the nearest cent.)\n a. $1,180.48\n b. $1,064.55\n c. $1,000.93\n d. $1,123.97

natasha had a $922.93 balance on her credit card at the beginning of september. her credit card has an apr of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. the following table shows natashas credit card purchases over the next two months.\n| month | cost ($) |\n| ---- | ---- |\n| september | 33.70 |\n| october | 61.70 |\n| october | 27.80 |\nif natasha makes only the minimum payments, what will her balance at the beginning of november? (assume that the interest accrues before the monthly payment, and that the monthly payment occurs at the end of the month. round all dollar values to the nearest cent.)\n a. $1,180.48\n b. $1,064.55\n c. $1,000.93\n d. $1,123.97

Answer

Explanation:

Step1: Calculate September's interest rate

The APR is 9.89%, so the monthly interest rate $r=\frac{9.89%}{12}=\frac{0.0989}{12}\approx0.008242$.

Step2: Calculate the balance at the end of September before payment

The initial balance in September is $B_0 = 922.93$, and the purchase in September is $P_1=33.70$. The balance before payment $B_1=(922.93 + 33.70)(1 + 0.008242)=956.63\times1.008242\approx964.43$.

Step3: Calculate September's minimum payment

The minimum - payment rate is 3.08%, so the September minimum payment $M_1 = 964.43\times0.0308\approx29.70$.

Step4: Calculate the balance after September's payment

The balance after payment $B_{1 - after}=964.43-29.70 = 934.73$.

Step5: Calculate October's balance before payment

The purchase in October is $P_2=61.70 + 27.80=89.50$. The balance before payment $B_2=(934.73+89.50)(1 + 0.008242)=1024.23\times1.008242\approx1032.65$.

Step6: Calculate October's minimum payment

The October minimum payment $M_2=1032.65\times0.0308\approx31.81$.

Step7: Calculate the balance at the beginning of November

The balance at the beginning of November $B = 1032.65-31.81=1000.84\approx1000.93$.

Answer:

c. $1,000.93$