Question

Jake owes $3,400 on his credit card. He is not charging any additional purchases because he wants to get this debt paid in full. The card has an APR of 13.2 percent. How much longer will it take him to pay off this balance if he makes monthly payments of $50 rather than $60?

Answer 1

Solution:
	Answer is 36.74 months
	longer will it take him to pay off this balance if he makes monthly payments of $50 rather than $60
Working Notes:
	credit card Loan amount $3,400 is the present value of all the payment done.
	present value of annuity = Px[ 1-(1 /(1 + i)^n)]/ i
P=Monthly payment = $60
	i= interest rate per period = 13.20%/12 = 1.1% = 0.011
	n= no. Of period = n months = ??
	PV of annuity= credit card balance $3,400
	present value of annuity = Px[ 1-(1 /(1 + i)^n)]/ i
	3400= 60 x (1-(1/(1+0.011)^n)/0.011
	(3400/60)x0.011 -1 = -(1/(1.011)^n)
	-0.3766666667 = - (1/(1.011)^n)
	0.3766666667 = (1/(1.011)^n)
	(1.011)^n = (1/0.3766666667)
	(1.011)^n =2.654867257
	taking log on both side
	log(1.011)^n = Log(2.654867257)
	n x Log (1.011) = Log(2.654867257)	using relation loga^b = b x Log a
	n = Log(2.654867257)/Log (1.011)
Notes:	Log values can be obtained from online calculators or excel
	For excel use this	=LOG(value)
	putting log values
	n= 0.424042811/ 0.004751156	Log(2.654867257) = 0.424042811
	n= 89.25045774 months	Log (1.011) = 0.004751156
	n= 89.25 months
P=Monthly payment = $50
	i= interest rate per period = 13.20%/12 = 1.1% = 0.011
	n= no. Of period = n months = ??
	PV of annuity= credit card balance $3,400
	present value of annuity = Px[ 1-(1 /(1 + i)^n)]/ i
	3400= 50 x (1-(1/(1+0.011)^n)/0.011
	(3400/50)x0.011 -1 = -(1/(1.011)^n)
	-0.252 = - (1/(1.011)^n)
	0.252 = (1/(1.011)^n)	-0.2520000
	(1.011)^n = (1/0.252)	-3.968253968
	(1.011)^n =3.968253968
	taking log on both side
	log(1.011)^n = Log(3.968253968)
	n x Log (1.011) = Log(3.968253968)	using relation loga^b = b x Log a
	n = Log(3.968253968)/Log (1.011)
Notes:	Log values can be obtained from online calculators or excel
	For excel use this	=LOG(value)
	putting log values
	n= 0.598599459/ 0.004751156	Log(3.968253968) = 0.598599459
	n= 125.9902767 months	Log (1.011) = 0.004751156
	n= 125.99 months
	longer will it take him to pay off this balance if he makes monthly payments of $50 rather than $60
	=Months at payment of $50 - Months at payment of $60
	=125.99 - 89.25
	=36.74 months
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