Question

PAYING OFF CREDIT CARDS Simon recently received a credit card with an 17% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $460. 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? Do not round intermediate calculations. Round your answer to the nearest month. month(s)

b.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 month. 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. Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

(a) Let number of months be N

r = 0.17/12 monthly

Monthly Payment = rP(1+r)^N/[(1+r)^N-1]

P = 460

Monthly Payment = 10

=> 10 = 460*(0.17/12)*(1+ 0.17/12)^N/((1+ 0.17/12)^N-1)

=> ((1+ 0.17/12)^N-1) = 0.6517(1+ 0.17/12)^N

N = 74.95 months or 75 months

(b) If Monthly Payment = 30,

30 = 460*(0.17/12)*(1+ 0.17/12)^N/((1+ 0.17/12)^N-1)

=> N = 17.40 months or 17 months

(c) Total Payments made in $10 plan = 10*74.95 = $749.5

Total Payments made in $30 plan = 30*17.40 = 522

Extra paid = $227.50