Answer:
- $249.72 more each month
- $962.82 less interest
Step-by-step explanation:
You want the difference in payments and in total interest paid if a $4500 credit card balance is paid off in 12 months instead of 36, given its interest rate is 19%.
Monthly payment
The amount of the monthly payment is given by the formula ...
[tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-n})}[/tex]
where P is the principal amount, r is the annual interests rate, and n payments are made.
The payment for the speedier payoff is ...
[tex]A=\dfrac{4500\cdot0.19}{12(1-(1+0.19/12)^{-12})}\approx414.70[/tex]
Increased payment amount
The amount by which the payment increases is ...
$414.70 -164.98 = $249.72
You must pay $249.72 more each month.
Interest expense
The amount you pay in interest is the difference between the total amount you pay and the initial balance:
(12 mo)×($414.705/mo) -4500 = 476.46
And the difference from the interest over 36 months is ...
$1439.28 - 476.46 = $962.82
You will pay about $962.82 less in total interest.
__
Additional comment
Above, and in the calculator computation attached, we have used the monthly payment amount without rounding to cents. It makes a total difference of about $0.06 in the computation of interest.
In reality, the interest is computed and rounded each month, so you can expect the result to differ by a few cents over the series of payments. The 12-month payment is rounded down here, so there will be a small final balance after the 12th payment.
The 36-month payment given is a few cents higher than the formula calculates ($164.952), so the interest given in the problem statement is likely high by about a dollar.
When trying to compute loan values accurate to cents, the best approach is one that uses a spreadsheet, computing the rounded interest and balance amounts after each payment.
