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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.



Card A Card B

Amount

$1,463.82 $1,157.98

APR

13% 17%

Monthly Payment

$24.60 $22.14


After 8 years, how much will Brandon have saved in interest by consolidating the two balances?

a. $581.76

b. $194.40

c. $256.32

d. $325.44

Respuesta :

RileyMyers

Answer:

(C) $256.32

Step-by-step explanation:

Lanuel

Brandon would save $256.12 in interest by consolidating the two balances on credit card A and B.

Given the following data:

  • Principal on Card A = $1,463.82.
  • APR on Card A = 13%.
  • Monthly payment on Card A = $24.60.
  • Principal on Card B = $1,157.98.
  • APR on Card B = 17%.
  • Monthly payment on Card B = $22.14.

How to calculate monthly payment.

Mathematically, the monthly payment for a credit card is given by this formula:

[tex]M=P(\frac{r}{1-(1+r)^{-nt}} )[/tex]

Where:

  • P is the principal.
  • r is the interest rate.
  • M is the monthly payment.
  • t is the time or number of years.
  • n is the number of times it's compounded.

Next, we would calculate the monthly payment for Card B at the lower interest rate (13%):

Note: [tex]r=13=\frac{0.13}{12} =0.01083333[/tex]

Substituting the given parameters into the formula, we have;

[tex]M=1157.98(\frac{0.01083333}{1-(1+0.01083333)^{-12\times 8}} )\\\\M=1157.98(\frac{0.01083333}{1-0.355437196} )\\\\M=1157.98(\frac{0.01083333}{0.644562804} )\\\\M=1157.98 \times 0.0168072528[/tex]

M = $19.47.

For the total payment:

Total payment = [tex]19.47 \times 96[/tex]

Total payment = $1,869.12.

For Card B at 17%:

Total payment B = [tex]22.14 \times 96[/tex]

Total payment B = $2,125.44.

For savings in interest:

Savings in interest = [tex]2125.44 - 1869.12[/tex]

Savings in interest = $256.12.

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