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 3004,300​, 2121​%; Card​ 2, ​$5 comma 8005,800​, 2525​%; and Card​ 3, ​$3 comma 1003,100​, 1717​%. Interest compounds monthly on all loan balances. A credit card loan consolidation company has captured​ Mary's attention by stating they can save Mary 2323​% per month on her credit card payments. This company charges 16.516.5​% APR. Is the​ company's claim​ correct? Assume a 1010​-year repayment period.

Answer 1

The claim is not rtue for Mary's financial situation

However, she will save up to 6.15% per month if the lona is taken.

Step-by-step explanation:

4,300 21 %

5,800 25 %

3,100 17 %

we will do interest expense per month under the current situation

and the situation if the loan is taken.

4,300 x 0.21/12 = 75.25

5,800 x 0.25/12 = 120.83

3,100 x 0.17/12 = 43.92

total interest 240

offer of 16.5% APR

4,300 + 5,800 + 3,100 = 13,200

we calculate the monthly cuota of a 10 year loan at 16.5% APR which present value is 13,200

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $13,200.00

time 120 (10 years x 12 months per year)

rate 0.01375 (0.165 / 12 month per year)

`13200 / (1-(1+0.01375)^(-120) )/(0.01375) = C\\`

C $ 225.25

Now we compare the savings:

240 - 225.25 = 14.75

14.75 / 240 = 0,0614583 = 6.15%