Question

In: Finance

a) You bought a $1200 TV with your new credit card that charges 23% APR. Your...

a) 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. (8 pt.s) a. How much is your monthly payment?

b. 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?

c. 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%?

Solutions

Expert Solution

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

please rate.


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