Question

Problem 37: Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased an Amazon Kindle for $350. The minimum payment on the card is only $10 per month a. If Simon makes minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? b. If Simon makes monthly payment of $30, how many months will it be before he pays off the debt? e How much more in total payments will Simon make under the $10-a-month plan than under the $30-a-month plan?

Answer 1

a). PV of Annuity = Monthly Payment * [{1 - (1 + r)^-n} / r]

$350 = $10 * [{1 - (1 + 0.18/12)^-n} / (0.18/12)]

$350 / $10 = {1 - (1.015)^-n} / 0.015

35 * 0.015 = 1 - (1.015)^-n

(1.015)^-n = 1 - 0.525

-n[log(1.015)] = log(0.475)

-n[0.0149] = -0.7444

n = -0.7444 / -0.0149 = 50 months

b). PV of Annuity = Monthly Payment * [{1 - (1 + r)^-n} / r]

$350 = $30 * [{1 - (1 + 0.18/12)^-n} / (0.18/12)]

$350 / $30 = {1 - (1.015)^-n} / 0.015

11.67 * 0.015 = 1 - (1.015)^-n

(1.015)^-n = 1 - 0.175

-n[log(1.015)] = log(0.825)

-n[0.0149] = -0.1924

n = -0.1924 / -0.0149 = 12.92 months

c). Total Amount Paid under $10-a-month plan = No. of Payments * Monthly Payment

= 50 * $10 = $500

Total Amount Paid under $30-a-month plan = No. of Payments * Monthly Payment

= 12.92 * $30 = $387.62

Difference = $500 - $387.62 = $112.38