Answer:
The balance will be less than $100 after 44 months payment
Explanation:
In this question, we are asked to calculate the time at which the Balance on a credit card would be less than $100.
To calculate this, we proceed as follows;
The monthly Interest rate = 23.9%/12 = 1.99166667%
Balance after t months = Credit Card balance * [(1 + Monthly interest rate ) * (1- Minimum payment rate)]^t
The credit card balance is $4,000, and the minimum payment rate is 5%
We plug these values into the equation to get;
$4,000 * [(1+1.99166667%) * (1 - 5%)]^t
= $4000 *[1.0199166667 * 0.95]^t
= $4000 * (0.968920836)^t
Balance after t months < 100
$4,000 * (0.968920836)^t < 100
(0.968920836)^t < 0.025
t = 43.9 months = 44 months
Answer: The balance will be less than $100 after 44 months.
Explanation:
We are to calculate the time when the balance on a credit card would be less than $100.
We were given the following:
APR = 23.9%
Monthly Interest rate will therefore be:
23.9%/12 = 1.99% or 0.0199
Credit card balance = $4,000
Minimum payment rate = 5% or 0.05
The formula is given as:
Balance after t months = Credit Card balance x [(1 + Monthly interest rate ) x (1- Minimum payment rate)]^t
Therefore:
$4,000 x [(1+0.0199) x (1 - 0.05)]^t
= $4000 x [1.0199 x 0.95]^t
= $4000 x (0.97)^t
Balance after t months < 100
= $4,000 x (0.97)^t < 100
= (0.97)^t < 100/4000
= (0.97)^t < 0.025
t = 43.9 months
t is therefore approximately 44 months.
