Assume that you have a balance of $5000 on your Discover credit card and that you make no more charges. Assume that Discover charges 27% APR and that each month you make only the minimum payment of 3.5% of the balance.
Find a formula for the balance B after t monthly payments. (Enter numerical values to four decimal places.)
((1 + 0.025) ( 1-0.035) = 0.9867125 = 0.9867
So I put 5000 x 0.9867t
Answer is wrong and I have no idea what they want.
You can do the following:
27% / 12 =0.0225 - This is your monthly interest rate. But your monthly payment is 3.5% of principal. So you can take the net of the two: 0.035 - 0.0225 =0.0125. Then you would use this rate to amortize the loan for t number of months as follows:
Balance =PV x [1 - 0.0125]^t
Balance =$5,000 x 0.9875^t
$0.01 =$5,000 x 0.9875^t
By the way, to bring down the balance of the loan to 1 cent, it would take about 366 months, or about 30.5 years!!.
CANNOT BE!! YOUR QUESTION IS WRONG!!!. Check your question carefully. Tell me your answer and I will show you how your question is wrong!
OK, young person! I think I figured out what your question should be. The minimum payment of 3.5% is to be applied to principal + Interest as follows:
27% / 12 + 1 = 1.0225
1 - 3.5% =0.965
1.0225 x 0.965 =0.9867125
Balance =5,000 x 0.9867125^t . So, this will give you the balance of the loan for any number of months.