frank has four different credit cards, the balances and interest information of which are outlined in the…

frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be?\n\n| credit card | balance | apr |\n| ---- | ---- | ---- |\n| a | $2,380 | 19% |\n| b | $4,500 | 15% |\n| c | $1,580 | 17.50% |\n| d | $900 | 21% |\n\na. $390.00\nb. $462.91\nc. $467.29\nd. $52.00

frank has four different credit cards, the balances and interest information of which are outlined in the table below. he would like to consolidate his credit cards to a single credit card with an apr of 18% and pay off the balance in 24 months. what will his monthly credit card payment be?\n\n| credit card | balance | apr |\n| ---- | ---- | ---- |\n| a | $2,380 | 19% |\n| b | $4,500 | 15% |\n| c | $1,580 | 17.50% |\n| d | $900 | 21% |\n\na. $390.00\nb. $462.91\nc. $467.29\nd. $52.00

Answer

Answer:

B. $462.91

Explanation:

Step1: Calculate total balance

$2380 + 4500+1580 + 900=9360$

Step2: Calculate monthly interest rate

The APR is 18%, so the monthly interest rate $r=\frac{0.18}{12}=0.015$

Step3: Use loan - payment formula

The loan - payment formula is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P$ is the principal amount (total balance), $r$ is the monthly interest rate, and $n$ is the number of payments. Here, $P = 9360$, $r=0.015$, and $n = 24$. $M=9360\times\frac{0.015\times(1 + 0.015)^{24}}{(1 + 0.015)^{24}-1}$ First, calculate $(1 + 0.015)^{24}\approx1.4295$ Then, $0.015\times(1 + 0.015)^{24}=0.015\times1.4295 = 0.0214425$ $(1 + 0.015)^{24}-1=1.4295 - 1=0.4295$ $\frac{0.015\times(1 + 0.015)^{24}}{(1 + 0.015)^{24}-1}=\frac{0.0214425}{0.4295}\approx0.049924$ $M = 9360\times0.049924\approx462.91$