Question

PAYING OFF CREDIT CARDS

Simon recently received a credit card with an 15% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $330. The minimum payment on the card is only $10 per month.

1. If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest month.
     month(s)

2. If Simon makes monthly payments of $30, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest month.
     month(s)

3. How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

a) Monthly interest rate = 15%/12 = 0.0125

Let the no of months be n for which Simon has to pay $10 each month to pay off the loan

10/0.0125*(1-1/1.0125^n) = 330

1-1/1.0125^n = 0.4125

1.0125^n = 1.702128

Taking natural log of both sides

n = ln(1.702128)/ln(1.0125) = 42.81 or 43 months

So, It will take Simon 43 months to pay off the card

b)

Let the no of months be n for which Simon has to pay $30 each month to pay off the loan

30/0.0125*(1-1/1.0125^n) = 330

1-1/1.0125^n = 0.1375

1.0125^n = 1.15942

Taking natural log of both sides

n = ln(1.15942)/ln(1.0125) = 11.90 or 12 months

So, It will take Simon 12 months to pay off the card

c) Total payments made for 43 months under $10 a month = $43*10 =$430

Total payments made for 12 months under $30 a month = $12*30 =$360

Extra payments made under the $10-a-month plan = $430-$360 = $70

(PS : The amounts are not exact as the months have been rounded off . Exact amount paid can be calculated as under

Extra amount paid in $ 10 a month plan in 43 months

= 10/0.0125*(1.0125^43-1) - 330*1.0125^43 = $1.83

So, exact amount paid in the plan = $10*43 - $1.83 = $428.17

Extra amount paid in $ 30 a month plan in 12 months

= 30/0.0125*(1.0125^12-1)- 330*1.0125^12 = $2.76

So, exact amount paid in the plan = $30*12 - $2.76 = $357.24

Extra amount paid in $10 plan as compared to $30 plan = $428.17-$357.24 = $70.93 )