Question

You bought a $1200 TV with your new credit card that charges 23% APR.  Your plan is to pay off the card in 5 years.  

1. How much is your monthly payment?  
2. After two years you plan to have better credit and use a card with a lower rate.  What will the balance be at this time?
3. If at the two year point, you can then afford to pay $45 per month, how many months will it take you to pay off the balance if the new rate is 12%?

Answer 1

a

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                              1,200
Rate of interest per period:
Annual rate of interest		23.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.23 /12 =	1.9167%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5.00
Total number of payments	N	5 × 12 =	60
Period payment using the formula	=	[ 1200 × 0.01917 × (1+0.01917)^60] / [(1+0.01917 ^60 -1]
Monthly payment	=	$                                                              33.83

b

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	1,200.00
Rate of interest	r=	1.9167%
nth payment	n=	24
Payment	P=	33.83
Loan balance	=	1200*(1+0.01917)^24 - 33.83*[(1+0.01917)^24-1]/0.01917
Loan balance	=	873.86

c

n	Number of payments required =	Log [ 1/ [1 - PV× r/ P] ]/ Log(1+r)
PV =	Present value	$                              873.86
P=	Periodic payment	45.00
r=	Rate of interest per period
	Annual interest	12.00%
	Number of payments per year	12
	Interest rate per period	0.12/12=
	Interest rate per period	1.000000%
	Number of payments =	Log [ 1/ (1- 873.86 × 0.01/45) ]/ Log( 1+ 0.01)
n=	Number of payments =	21.70

It takes 21.7 months

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