Simon recently received a credit card with an 18% nominal interest rate. With the card, he purchased an Apple iPhone 5 for $360. The minimum payment on the card is only $20 per month.
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)
If Simon makes monthly payments of $60, 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)
How much more in total payments will Simon make under the $20-a-month plan than under the $60-a-month plan. Do not round intermediate calculations. Round your answer to the nearest cent.
a) Purchase amount of phonw (PV) = 360
Minimum Payment (PMT) = 20
rate per month = 18%/12 = 1.5%
PV = PMT *( 1- (1+r)-n)/r
360 = 20 * ( 1 - (1+1.5%)-n)/1.5%
1- 18*1.5% = 1.015-n
1.1015-n = 0.73
log 1.1015-n = log0.73
-n = Log 0.73/log1.1015
n = 21.1377 or 21 months
b) Purchase amount of phonw (PV) = 360
Minimum Payment (PMT) = 60
rate per month = 18%/12 = 1.5%
PV = PMT *( 1- (1+r)-n)/r
360 = 60 * ( 1 - (1+1.5%)-n)/1.5%
1- 6*1.5% = 1.015-n
1.1015-n = 0.91
log 1.1015-n = log0.91
-n = Log 0.91/log1.1015
n = 6.33442 or 6 months
More Payment for S20 plan over 60$ plan = 20* 21.1377 -60*6.33442 =
42.69
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