Question

​Mary's credit card situation is out of control because she cannot afford to make her monthly payments. She has three credit cards with the following loan balances and​ APRs: Card​ 1, ​$4 comma 700​, 20​%; Card​ 2, ​$5 comma 500​, 24​%; and Card​ 3, ​$3 comma 300​, 16​%. Interest compounds monthly on all loan balances. A credit card loan consolidation company has captured​ Mary's attention by stating they can save Mary 22​% per month on her credit card payments. This company charges 17.5​% APR. Is the​ company's claim​ correct? Assume a 10​-year repayment period.

Answer 1

Answer:

Ans. No, with the new deal from the credit card consolidation company, she´d save $28.45, which is 10.64%, not 22%.

Explanation:

Hi, first, we need to find out how much she has to pay with the present obligations, to do this, we need to divide every APR by 12 so we can make it effective monthly, the years to pay, have to be multiplied by 12 in order to get how many payments she has to make (in all cases that is 10years * 12 = 120) and then, use the following formula, and solve for "A".

$PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

A= Payment

r = rate

n = 120 months

So let´s find out how much she has to pay every month, for 10 years for each of her obligations.

Credit card 1.

$4,700=\frac{A((1+0.0167)^{120}-1) }{0.0167(1+0.0167)^{120} }$

$4,700=A(51.74492364)$

$A(1)= 90.83$

Credit card 2.

$5,500=\frac{A((1+0.02)^{120}-1) }{0.02(1+0.02)^{120} }$

$5,500=A(45.3553885)$

$A(2)= 121.26$

Credit card 3.

$3,300=\frac{A((1+0.0133)^{120}-1) }{0.0133(1+0.0133)^{120} }$

$3,300=A(59.69681612)$

$A(3)= 55.28$

If we add them up together, we get $267.37

Now, let´s suppose that she makes the decision of transfer all her obligations to this consolidation company, what we have is:

$13,500=\frac{A((1+0.01458)^{120}-1) }{0.01458(1+0.01458)^{120} }$

$13,500=A(56.50395555)$

$A(n)=238.92$

now, let´s see how much she is saving in percentage in her monthly payment.

$Percentage=\frac{(FinalValue-InitialValue)}{InitialValue} =\frac{(238.92-267.37}{267.37} =-0.1064$

So, if she goes and consolidate her loans in this company, she is going to save 10.64% every month on their monthly payment, not 22%.

Best regards.