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, ​$4,700​, 19​%; Card​ 2, ​$5,500​, 23​%; and Card​ 3, ​$3,100​, 17​%. Interest compounds monthly on all loan balances. A credit card loan consolidation company has captured​ Mary's attention by stating they can save Mary 24​% per month on her credit card payments. This company charges 15.5​% APR. Is the​ company's claim​ correct? Assume a 10​-year repayment period.

a) ​Mary's current minimum monthly payments are?

b) Mary's minimum monthly payments after loan consolidation will be?

Answer 1

t = 10 * 12 = 120 months

Formula (A/P,i%,n) = i((1 + i)^n)/((1 + i)^n-1)

Credit card 1

i = 19% / 12= 1.5833% per month

Monthly loan payment = 4700 * (A/P,1.5833%,120)

= 4700 * 0.015833 * ((1 + 0.015833)^120)/((1 + 0.015833)^120-1)

= 4700 * 0.015833 * ((1.015833)^120)/((1.015833)^120-1)

= 4700 * 0.018667

= 87.7349

Credit card 2

i = 23% / 12= 1.9167% per month

Monthly loan payment = 5500 * (A/P,1.9167%,120)

= 5500 * 0.019167 * ((1 + 0.019167)^120)/((1 + 0.019167)^120-1)

= 5500 * 0.019167 * ((1.019167)^120)/((1.019167)^120-1)

= 5500 * 0.021355

= 117.4525

Credit card 3

i = 17% / 12= 1.4167% per month

Monthly loan payment = 3100 * (A/P,1.4167%,120)

= 3100 * 0.014167 * ((1 + 0.014167)^120)/((1 + 0.014167)^120-1)

= 3100 * 0.014167 * ((1.014167)^120)/((1.014167)^120-1)

= 3100 * 0.017380

= 53.878

Total current monthly payment = 87.7349 + 117.4525 + 53.878 = 259.06

b.

Total loan = 4700 + 5500 + 3100 = 13300

i = 15.5% / 12 = 1.2917%

Monthly loan payment = 13300 * (A/P,1.2917%,120)

= 13300 * 0.012917 * ((1 + 0.012917)^120)/((1 + 0.012917)^120-1)

= 133300 * 0.012917 * ((1.012917)^120)/((1.012917)^120-1)

= 13300 * 0.016441

= 218.6653 ~ 218.67

Claim of savings of 24% is worng as 24% of 259.06 = 62.17

And current savings after loan consolidation = 259.06 - 218.67 = 40.39

So claim is wrong