brandon has two credit cards and would like to consolidate the two balances into one balance on the card…

brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards brandon currently uses.\n| |card a|card b|\n|--|--|--|\n|amount|$1,463.82|$1,157.98|\n|apr|13%|17%|\n|monthly payment|$24.60|$22.14|\nafter 8 years, how much will brandon have saved in interest by consolidating the two balances?\n a. $581.76\n b. $194.40\n c. $256.32\n d. $325.44

brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards brandon currently uses.\n| |card a|card b|\n|--|--|--|\n|amount|$1,463.82|$1,157.98|\n|apr|13%|17%|\n|monthly payment|$24.60|$22.14|\nafter 8 years, how much will brandon have saved in interest by consolidating the two balances?\n a. $581.76\n b. $194.40\n c. $256.32\n d. $325.44

Answer

Explanation:

Step1: Calculate total payments for Card A

Number of months in 8 years is $n = 8\times12=96$ months. Total payment for Card A is $P_A=24.60\times96 = 2361.6$. Interest paid on Card A is $I_A=2361.6 - 1463.82=897.78$.

Step2: Calculate total payments for Card B

Total payment for Card B is $P_B=22.14\times96=2125.44$. Interest paid on Card B is $I_B=2125.44 - 1157.98 = 967.46$.

Step3: Calculate total interest without consolidation

Total interest without consolidation is $I_{total1}=I_A + I_B=897.78+967.46 = 1865.24$.

Step4: Calculate total balance

Total balance is $B = 1463.82+1157.98=2621.8$.

Step5: Calculate monthly payment and interest for consolidated balance on lower - rate card

Using the formula for the monthly payment of a loan $M=\frac{P\times r\times(1 + r)^n}{(1 + r)^n-1}$, where $P = 2621.8$, $r=\frac{0.13}{12}$, and $n = 96$. First, calculate $(1 + r)^n=(1+\frac{0.13}{12})^{96}\approx2.307$. Then $M=\frac{2621.8\times\frac{0.13}{12}\times2.307}{2.307 - 1}\approx43.57$. Total payment for the consolidated loan is $P_{consolidated}=43.57\times96 = 4182.72$. Interest paid on the consolidated loan is $I_{consolidated}=4182.72-2621.8 = 1560.92$.

Step6: Calculate interest saved

Interest saved is $I_{saved}=1865.24 - 1560.92=304.32$. There may be some rounding - error differences. Let's calculate in another way. We can also use the simple - interest approximation (less accurate but for a quick check). Interest on Card A without consolidation: $I_{A1}=1463.82\times0.13\times8=1522.37$. Interest on Card B without consolidation: $I_{B1}=1157.98\times0.17\times8 = 1576.82$. Total interest without consolidation $I_{total2}=1522.37+1576.82=3099.19$. Total balance $B = 2621.8$. Interest on consolidated balance at 13%: $I_{consolidated2}=2621.8\times0.13\times8=2726.67$. Interest saved $I_{saved2}=3099.19 - 2726.67 = 372.52$. The more accurate way is using the loan - payment formula. The closest answer to our accurate calculation is d.

Answer:

d. $325.44$