Interest/APR/credit card math problem...something like that? [for a high school pre-calculus student]?
Here's the question:
You have credit card charges totaling $15,750. The interest rate of your card is 10.5% APR. They tell you the minimum payment is $135. The amount of interest due each month is figured as:
Current Balance x (yearly APR/1200)
(Here the APR is not changed to a decimal.) The remaining amount is applied to lowering the principal (the current balance).
1. Make a table that shows the months, the interest paid, and the new current balance. Use a computer spreadsheet with the following headings:
Month / Current Balance / Interest / Amt applied to principal
2. Will you ever get out of debt with the credit card company? If so, when? If no, why not?
3. Make a new table with a minimum payment of $150
a. Will you ever be out of debt?
b. If not, why not? If so, when?
c. How much interest will you have paid over the time of the loan?
Formulas to use for 3b and 3c:
3b. U = M- (M-Pr/12) (1+r/12)^12t
U= unpaid balance
M= monthly payment
P= amount borrowed
t= time (years)
r= rate (decimal form)
3c. U= P [rt/1-(1/1+r/12)^12t -1]
U= total interest paid
CAN SOMEONE PLEASE EXPLAIN THIS MESS TO ME?!?!?
Answer
There's a lot here -- I'm going to start (I never know if people really check back). I'll assume you know some spreadsheet lingo.
Put the titles (Month, Balance, etc.) in row 1 columns A, B, C, D.
Start with 0 (month 0) in A2
Start with the 15,750 (balance) in B2.
Put 0 in C2 and D2 (nothing's happened yet).
That completes row 2, which is just the initial balance.
Row 3 is month 1. Put 1 (month 1) in A3. The interest (C3) is going to be the old balance (B2) times the interest rate (10.5/1200). So C3 is +B2*10.5/1200.
The new balance (B3) is the old balance (B2) plus the interest (C3) minus the payment (135). So B3 = +B2+B3-135.
The amount paid to the principal (D3) is the payment (135) less what went to interest (C3) so D3 is =135-C3.
That completes row 3.
You now can copy row 3 down (spreadsheet lingo) to find out how it will go in the future. And the miracles of spreadsheets work.
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