Question

Michelle has four credit cards with the balances and interest rates listed below. She would like to consolidate all of her credit cards in a single credit card with an interest rate of 16% and pay off the balance in 36 months. If she did so, what would Michelle’s monthly credit card payment be?

Credit Card
Balance
APR
#1
$4,380
17%
#2
$1,365
19%
#3
$2,480
23%
#4
$5,000
15%
a.
$367.36
b.
$464.95
c.
$685.23
d.
$826.56

Answer 1

mark me brilliant

Explanation:

To calculate Michelle’s monthly credit card payment, we need to find the total amount she owes and then divide it by the number of months she has to pay it off.

First, we need to find the total balance on Michelle’s credit cards:

$4,380 + $1,365 + $2,480 + $5,000 = $13,225

Next, we need to find the weighted average interest rate of her credit cards. To do this, we multiply each balance by its corresponding APR and add up the results. Then we divide by the total balance:

($4,380 x 0.17) + ($1,365 x 0.19) + ($2,480 x 0.23) + ($5,000 x 0.15) = $1,038.55

$1,038.55 ÷ $13,225 = 0.0785, or 7.85%

Now we can use the total balance and the weighted average interest rate to calculate Michelle’s monthly payment using the formula for a fixed payment on a loan:

P = (r(PV)) / (1 - (1 + r)^-n)

Where:

P = monthly payment

r = monthly interest rate (as a decimal)

PV = present value of the loan

n = number of payments

r = 0.16 ÷ 12 = 0.01333 (monthly interest rate)

PV = $13,225

n = 36

P = (0.01333(13,225)) / (1 - (1 + 0.01333)^-36) = $367.36

Therefore, Michelle’s monthly credit card payment would be $367.36 if she consolidated all of her credit card debt into a single credit card with an interest rate of 16% and paid it off in 36 months. The answer is (a) $367.36.