Question

5-2: Future Values 5-15: Semiannual and Other Compounding periods 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 $320. The minimum payment on the card is only $10 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? Round your answer to the nearest whole. month(s) b. If Simon makes monthly payments of $30, how many months will it be before he pays off the debt? Round your answer to the nearest whole. month(s) C. How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan. Make sure you use 3 decimal places for N. Round your answer to the nearest cent.

Answer 1

a). Monthly Payment = [Borrowed Amount * r] / [1 - (1 + r)^-n]

$10 = [$320 * (0.15/12)] / [1 - {1 + (0.15/12)}^-n]

1 - {1.0125}^-n = $4 / $10

{1.0125}^-n = 1 - 0.4

-n[log(1.0125)] = log[0.6]

-n[0.0124] = -0.5108

n[0.0124] = 0.5108

n = 0.5108 / 0.0124 = 41.12, or 41 months

b). Monthly Payment = [Borrowed Amount * r] / [1 - (1 + r)^-n]

$30 = [$320 * (0.15/12)] / [1 - {1 + (0.15/12)}^-n]

1 - {1.0125}^-n = $4 / $30

{1.0125}^-n = 1 - 0.1333

-n[log(1.0125)] = log[0.8667]

-n[0.0124] = -0.1431

n[0.0124] = 0.1431

n = 0.1431 / 0.0124 = 11.52, or 12 months

c). Total payments @$10/month = Number of payments * Monthly Payment

= 41.121 * $10 = $411.21

Total payments @$30/month = Number of payments * Monthly Payment = 11.520 * $30 = $345.58

Extra Interest = Total payments @$10/month - Total payments @$30/month

= $411.21 - $345.58 = $65.63