Question

Simon recently received a credit card with a 12% nominal interest rate. With the card, he purchased an Apple iPhone 7 for $353.81. 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 $35, 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 $35-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

Answer 1

Purchase price of Iphone = $ 353.81

As, Simon will pay $ 10 per month to pay back the credit card payment to buy Iphone, we will take Iphone cost as Present value.

1). Calculating the no of months for SIMOn to pay back off the card using Present Value of Ordinary annuity:-

Where, C= Periodic Payments = $10

r = Periodic Interest rate = 0.12/12 = 0.01

n= no of periods

Present Value = $ 353.81

(1.01)^-n = 1-0.35381

(1.01)^-n = 0.64619

Taking log both sides,

-nlog(1.01) = log(0.64619)

Solving value of log from financial calculator:-

-n(0.0043213738) = -0.1896397671

n = 44

So, it will take 44 months to pay off the credit credit payments.

2) Now replacing , monthly payment of $ 10 with $ 10.

Calculating the no of months for SIMOn to pay back off the card using Present Value of Ordinary annuity:-

Where, C= Periodic Payments = $35

r = Periodic Interest rate = 0.12/12 = 0.01

n= no of periods

Present Value = $ 353.81

(1.01)^-n = 1-0.10108857142

(1.01)^-n = 0.89891142858

Taking log both sides,

-nlog(1.01) = log(0.89891142858)

Solving value of log from financial calculator:-

-n(0.0043213738) = -0.04628309800

n = 11

So, it will take 11 months to pay off the credit credit payments.

c). Total Payment when $ 10 per month paid = $10*44 months

= $ 440

Total Payment when $ 35 per month paid = $35*11 months

= $ 385

So, extra payment being made under $ 10 plan than in $ 35 plan = $ 440 - $385

= $55

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