Question

Simon recently received a credit card with an 13% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $460. The minimum payment on the card is only $20 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 $60, 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 $20-a-month plan than under the $60-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.
   $

Answer 1

a. Information provided:

Present value= $460

Monthly payment= $20

Monthly interest rate= 13%/12= 1.0833%

The time to pay off the card is calculated by entering the below in a financial calculator:

PV= -460

PMT= 20

I/Y= 1.0833

Press the CPT key and N to compute the time to pay off the card.

The value obtained is 26.60.

Therefore, it will take 27 months to pay off the debt if the monthly payment is $20.

b. Information provided:

Present value= $460

Monthly payment= $60

Monthly interest rate= 13%/12= 1.0833%

The time to pay off the card is calculated by entering the below in a financial calculator:

PV= -460

PMT= 60

I/Y= 1.0833

Press the CPT key and N to compute the time to pay off the card.

The value obtained is 8.0471.

Therefore, it will take 8 months to pay off the debt if the monthly payment is $60.

c.Total payments under the $20 a month plan= $20*27= $540

Total payments under the $60 a month plan= $60*8= $480

= $540 - $480

= $60

Therefore, Simon will have to pay $60 more in total payments under the 20 a month plan than under the $60 a month plan

In case of any query, kindly comment on the solution.