I know this isn't a degree related but I would be happy if someone could help me. Is anyone good at doing math? I have a question that's driving me crazy and quite frankly three maths faculty at my school. I know the answer to the problem but don't know to show the working without doing a long amortization. XYZ is paying off a credit card with a current balance of $450. The interest rate on the card is 23% (annually). The minimum payment is $25, but XYZ plans to make monthly payments of $45. XYZ will not be using the card to accumulate more debt. Approximately how many months will it take to pay off the balance? The answer is 11. I just need a shorter way to show my answer.
I see that you are calculating starting at month 1. If I understand the problem correctly, I think it makes more sense to start at month 0 then calculate interest and payment every month from month 0. From here, we just make a formula. Set one side equal to zero because we know that we're looking for $0 balance. Monthly interest is .23 = 23/100 per year, so for each month: 23/100/12 = (23/100) * (1/12 )= 23/1200 monthly interest rate Since we're adding interest each month, we set it to the power of m, the number of months. Since we're paying $45 each month, we subtract 45m. 0 = 450(1+23/1200)^m - 45m Simplify by adding the two terms in the parentheses. Simplify by dividing by the common factor of 45. 0 = 10(1223/1200)^m - m Then additive inverse give us: m = 10(1223/1200)^m Now we know what m is! Well, sort of. We still have an m on both sides and it would only get more complicated from here if we try to solve it algebraically. So, let's cut right to the chase and just graph the thing. You can do this by setting BOTH variables equal to m. let y = m let x = m Why? Because now, not only is this equation true: y = 10(1223/1200)^x But then we also know that THIS equation is true: y = x The solution to the system of equations is the point on a graph where the lines intersect. Plug them both into a graphing calculator and you find that they intersect at (12.735, 12.735). Ergo, you will pay off the debt entirely after 13 months. That is, if my math is correct
Use the most difficult, lengthy calculation process you can think of. And do it with no calculator. Try doing it in your head. That way, you will NEVER want to solve a problem like this again - and you will avoid credit card debt like the plague it is. I once did a calculation involving a high balance and low minimum payment on a bank credit card. Payout took something like 27 years! I worked in the credit card business for over 20 years and that's why I carry no credit cards at all. I have one prepaid card that is the only way I can get stuff on the Internet - with my own money. In stores, I use a debit card - again, to spend my own money.
Thanks for the responses. I taught my students the amortization model (as shown on my attachment) to solve that problem. I teach Financial Management so I think that's the best way to teach them rather than get into algebra and calculus... lol
