Question

Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased an Apple iPhone 7 for $384.43. The minimum payment on the card is only $20 per month. a. 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) b. If Simon makes monthly payments of $65, 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) c. How much more in total payments will Simon make under the $20-a-month plan than under the $65-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Compute the monthly rate of interest, using the equation as shown below:

Monthly rate = Annual rate/ 12

                      = 18%/ 12

                      = 1.5%

Hence, the monthly rate of interest is 1.5%.

(a)

Compute the number of payments required to pay off the loan, using the equation as shown below:

Loan amount = Monthly payment*{1 – (1 + Rate)^{-Number of periods}}/ Rate

            $384.43 = $20*{1 – (1 + 0.015)^{-Number of periods}}/ 1.5%

Rearrange the above mentioned equation to determine the number of payment periods as follows:

1 – (1 + 0.015)^{-Number of periods} = $384.43*1.5%/ $20

(1.015)^{-Number of periods} = 0.7116775

After solving the above-mentioned equation, the number of payment periods comes out to be 23 months.

(b)

Compute the number of payments required to pay off the loan, using the equation as shown below:

Loan amount = Monthly payment*{1 – (1 + Rate)^{-Number of periods}}/ Rate

            $384.43 = $65*{1 – (1 + 0.015)^{-Number of periods}}/ 1.5%

Rearrange the above-mentioned equation to determine the number of payment periods as follows:

1 – (1 + 0.015)^{-Number of periods} = $384.43*1.5%/ $65

(1.015)^{-Number of periods} = 0.91128538462

After solving the above-mentioned equation, the number of payment periods comes out to be 6 months.

(c)

Compute the extra payment made by Simon, using the equation as shown below:

Extra payment = (Monthly payment of $20*Number of months) – (Monthly payment of 65*Number of months)

                           = ($20*23 months) – ($65*6)

                           = $70

Hence, the extra payment made by Simon is $70.