In: Finance
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%?
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.