SOLUTION: You have $2,000 on a credit card that charges a 22% interest rate. If you want to pay off the credit card in four years, how much will you need to pay each month (assuming you don'

Algebra ->  Finance -> SOLUTION: You have $2,000 on a credit card that charges a 22% interest rate. If you want to pay off the credit card in four years, how much will you need to pay each month (assuming you don'      Log On


   

Question 1181529: You have $2,000 on a credit card that charges a 22% interest rate. If you want to pay off the credit card in four years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to calculate the monthly payment you'll need to make to pay off your $2,000 credit card balance in four years with a 22% interest rate:
**1. Convert the annual interest rate to a monthly rate:**
* Monthly interest rate = (Annual interest rate) / 12
* Monthly interest rate = 22% / 12 = 0.22 / 12 = 0.018333 (approximately)
**2. Calculate the number of monthly payments:**
* Number of payments = (Number of years) * 12
* Number of payments = 4 * 12 = 48
**3. Use the loan payment formula:**
The formula to calculate the monthly payment (M) is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where:
* M = Monthly payment
* P = Principal balance ($2,000)
* i = Monthly interest rate (0.018333)
* n = Number of payments (48)
**4. Plug in the values and calculate:**
M = 2000 [ 0.018333 (1 + 0.018333)^48 ] / [ (1 + 0.018333)^48 - 1]
M = 2000 [ 0.018333 (1.018333)^48 ] / [ (1.018333)^48 - 1]
M = 2000 [ 0.018333 * 2.382769] / [2.382769 - 1]
M = 2000 [0.043697] / [1.382769]
M = 2000 * 0.031599
M ≈ $63.20
**Therefore, you will need to pay approximately $63.20 each month to pay off your credit card balance in four years.**

Answer by ikleyn(52894) About Me  (Show Source):
You can put this solution on YOUR website!
.
You have $2,000 on a credit card that charges a 22% interest rate.
If you want to pay off the credit card in four years, how much will you need to pay
each month (assuming you don't charge anything new to the card)?
~~~~~~~~~~~~~~~~~~~~~~~~~ 

It is the same as if you took a loan of $2000, and you want to pay it off 
in 4 years at 22% annual interest rate compounded montly.


Use the formula for the monthly payment for a loan

    M = L%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29


where L is the loan amount; r = 0.22%2F12 is the effective interest rate per month;
n is the number of payments (same as the number of months in 4 years); M is the monthly payment.


In this problem  L = $2000;  r = 0.1%2F12;  n = 4*12 = 48.


Substitute these values into the formula and get for monthly payment

    M = 2000%2A%28%28%280.22%2F12%29%29%2F%281-%281%2B0.22%2F12%29%5E%28-48%29%29%29 = $63.01  (rounded).


Thus, the monthly payment is $63.01.    ANSWER

Solved.