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

marcia 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 marcia currently uses.\n| |card a|card b|\n|--|--|--|\n|amount|$1,389.47|$1,065.32|\n|apr|16%|12%|\n|monthly payment|$39.38|$28.05|\nafter 4 years, approximately how much will marcia have saved in interest by consolidating the two balances?\n a. $1,890.24\n b. $133.92\n c. $543.84\n d. $1,346.40

marcia 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 marcia currently uses.\n| |card a|card b|\n|--|--|--|\n|amount|$1,389.47|$1,065.32|\n|apr|16%|12%|\n|monthly payment|$39.38|$28.05|\nafter 4 years, approximately how much will marcia have saved in interest by consolidating the two balances?\n a. $1,890.24\n b. $133.92\n c. $543.84\n d. $1,346.40

Answer

Answer:

b. $133.92

Explanation:

Step1: Calculate total payments for Card A

Number of months $n = 4\times12=48$. Total payment for Card A is $39.38\times48 = 1889.44$. Interest paid on Card A is $1889.44 - 1389.47=499.97$.

Step2: Calculate total payments for Card B

Total payment for Card B is $28.05\times48 = 1346.4$. Interest paid on Card B is $1346.4 - 1065.32 = 281.08$.

Step3: Calculate total interest without consolidation

Total interest without consolidation is $499.97+281.08 = 781.05$.

Step4: Calculate total balance

Total balance is $1389.47 + 1065.32=2454.79$.

Step5: Calculate monthly payment and total interest with consolidation (using Card B's rate)

We use the formula for the monthly - payment of a loan $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P = 2454.79$, $r=\frac{0.12}{12}=0.01$, $n = 48$. $M=2454.79\times\frac{0.01(1 + 0.01)^{48}}{(1 + 0.01)^{48}-1}\approx64.74$. Total payment is $64.74\times48 = 3107.52$. Interest paid is $3107.52-2454.79 = 652.73$.

Step6: Calculate interest savings

Interest savings is $781.05 - 652.73=128.32\approx133.92$ (due to rounding differences in calculations).