Question

Simon recently received a credit card with a 19% nominal interest rate. With the card, he purchased an Apple iPhone 7 for $440.00. 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 whole number.
     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 whole number.
     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.Information provided:

Present value (PV)= $440

Monthly payment= $10

Monthly market rate= yield to maturity (I/Y)= 19%/12= 1.5833% per month

The time taken to payoff the card is calculated by entering the below information in a financial calculation:

PV= -440

PMT= 10

I/Y= 1.5833

Press the CPT key and N to compute the time taken to payoff the card

The value obtained is 75.94.

Therefore, it takes 75.94 months to payoff the card.

b.Information provided:

Present value (PV)= $440

Monthly payment= $30

Monthly market rate= yield to maturity (I/Y)= 19%/12= 1.5833% per month

The time taken to payoff the card is calculated by entering the below information in a financial calculation:

PV= -440

PMT= 30

I/Y= 1.5833

Press the CPT key and N to compute the time taken to payoff the card.

The value obtained is 16.82.

Therefore, it takes 16.82 months to payoff the card.

c.Difference in total payments:

= $10*75.94 - $30*16.82

= $759.40 - $504.60

= $254.80

Therefore, Simon will have pay $254.80 more in total payments under the $10 a month plan than under $30 a month plan.

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