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

natasha had a $922.93 balance on her credit card at the beginning of september. her credit card has an apr of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. the following table shows natashas credit card purchases over the next two months. month cost ($) september 33.70 october 61.70 october 27.80 if 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.) a. $1,180.48 b. $1,064.55 c. $1,000.93 d. $1,123.97

natasha had a $922.93 balance on her credit card at the beginning of september. her credit card has an apr of 9.89%, compounded monthly, and a minimum monthly payment of 3.08% of the total balance. the following table shows natashas credit card purchases over the next two months. month cost ($) september 33.70 october 61.70 october 27.80 if 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.) a. $1,180.48 b. $1,064.55 c. $1,000.93 d. $1,123.97

Answer

Answer:

b. $1,064.55

Explanation:

Step1: Calculate September balance before payment

The initial balance in September is $922.93. The purchase in September is $33.70. The monthly - interest rate $r=\frac{9.89%}{12}=\frac{0.0989}{12}$. The balance before payment in September, $B_1=(922.93 + 33.70)(1+\frac{0.0989}{12})=(956.63)(1+\frac{0.0989}{12})\approx956.63\times1.008242\approx964.40$.

Step2: Calculate September payment

The minimum monthly payment in September is $P_1 = 0.0308\times964.40\approx29.70$. The balance after payment in September, $B_{1 - after}=964.40-29.70 = 934.70$.

Step3: Calculate October balance before payment

The purchases in October are $61.70 + 27.80=89.50$. The balance before payment in October, $B_2=(934.70 + 89.50)(1+\frac{0.0989}{12})=(1024.20)(1+\frac{0.0989}{12})\approx1024.20\times1.008242\approx1032.69$.

Step4: Calculate October payment

The minimum monthly payment in October is $P_2=0.0308\times1032.69\approx31.81$. The balance at the beginning of November, $B = 1032.69-31.81=1064.55$.