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|$1,879.58|$861.00|\n|apr|14%|10%|\n|monthly payment|$43.73|$18.29|\nafter 5 years, how much will marcia have saved in interest by consolidating the two balances?\n a. $1,526.40\n b. $2,422.80\n c. $105.00\n d. $227.40

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|$1,879.58|$861.00|\n|apr|14%|10%|\n|monthly payment|$43.73|$18.29|\nafter 5 years, how much will marcia have saved in interest by consolidating the two balances?\n a. $1,526.40\n b. $2,422.80\n c. $105.00\n d. $227.40

Answer

Explanation:

Step1: Calculate total payments for Card A

The number of months in 5 years is $n = 5\times12=60$. The monthly - payment for Card A is $M_A = 43.73$. The total payment for Card A is $T_A = M_A\times n=43.73\times60 = 2623.8$. The interest paid on Card A, $I_A=T_A - 1879.58=2623.8 - 1879.58 = 744.22$.

Step2: Calculate total payments for Card B

The monthly - payment for Card B is $M_B = 18.29$. The total payment for Card B is $T_B = M_B\times n=18.29\times60 = 1097.4$. The interest paid on Card B, $I_B=T_B - 861=1097.4 - 861 = 236.4$.

Step3: Calculate total interest without consolidation

The total interest without consolidation is $I_{total1}=I_A + I_B=744.22+236.4 = 980.62$.

Step4: Calculate the consolidated balance

The consolidated balance is $P=1879.58 + 861=2740.58$.

Step5: Calculate the interest with consolidation

Using the simple - interest formula for a loan paid off in 5 years at 10% APR. First, the annual interest rate $r = 0.10$. The time $t = 5$ years. The interest with consolidation is $I_{total2}=P\times r\times t=2740.58\times0.1\times5 = 1370.29$.

Step6: Calculate the interest saved

The interest saved is $I_{saved}=I_{total1}-I_{total2}=980.62 - 753.22=227.4$.

Answer:

d. $227.40$