This week, our focus will be on amortized loans. Most loans that you take out will be amortized loans - mortgages, student loans, car loans, furniture loans, etc. Last week we learned how to determine the payment on an amortized loan. This week, we'll be focusing on answering several questions.
1. If you know how much you can afford to pay each month and you know the rate and term of the loan, how much can you afford to borrow?
2. Suppose you are several years into a given loan and you are offered to refinance to another loan at a different rate. What does it mean to refinance? Will this particular offer save you money?
3. Suppose you pay extra each month on your amortized loan. How much will you save in interest by paying ahead? How soon will you pay off the loan?
These are all very interesting questions to ask when you are looking at a loan. Question 1 simply requires you to solve for P in the formula below. Questions 2 and 3 will require a little more thought before we can solve them.
\[ P = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-mt}}{\frac{r}{m}}\right] \]
We will be learning how to use the formula to answer the questions above by hand. However, there are many calculators online to help answer these questions and more about taking out a loan. Below are links to some calculators that you may find useful when you want to consider taking out a loan in the future.
Bankrate.com
Amortization Schedule Calculator
Mortgage Payoff Calculator
Cost of Living Calculator
Is it Better to Rent or Buy?
We will only be considering fixed rate loans in all of our examples. But lenders may also offer you an adjustable rate mortgage (ARM). As the name suggests, with an adjustable rate mortgage, your rate can change, depending on market rates. These loans can be risky - if rates go up, so does your monthly payment.
Challenge Problem: (Due Wednesday, April 12) Determine what kind of job you want to have after you graduate. Research salaries for this job in your dream town. Using a home affordability calculator, determine how expensive a house you could afford based on this salary. Then, go to zillow.com, and choose a home to purchase (in your budget) in your dream town. Looking at current interest rates, choose a loan. Given this loan, calculate the following by hand. (You may use the online calculator to check your answers, but you must also work out the answers by hand.)
1. Your monthly payments.
2. The amount of interest you would pay by just making the minimal monthly payments.
3. The amount of interest you would pay by paying an extra $100 each month and how soon you would be able to pay off the loan.
4. The amount of interest you would pay by paying an extra $250 each month and how soon you would be able to pay off the loan.
Include the resources you used to determine your future salary, home affordability, loan terms, and the zillow page for the home you chose.
for the amortization schedules,to find the new balance after each payment do we first have to find the initial payment? and if so how do we do that? (questions 8 through 10 on bank 2 of webwork)
ReplyDeleteYou do. You can find the payment by plugging into the formula for amortized loans and solving for R. You'll need to find all entries in the amortization schedule to get the new balance. The webwork questions just require you to enter those new balances from the last column of your amortization schedule.
DeleteI am glad that we are learning about loans and refinancing them to get a better interest rate. This is what we all need to know and they are pretty easy to figure out once you get the hang of it.
ReplyDeleteThis is by far my favorite thing we have learned in class. I see myself using this for future investments and to budget for home improvements. The only real problem I am having is solving for t or r in the compound continuous equations. It is also jaw dropping to see how much interest is paid at the beginning of a mortgage. I just bought my first house a couple months ago and learning this math has motivated me to pay more towards the principal of the loan than just paying the minimum.
ReplyDeleteI am having trouble with solving the problems. I am able to plug everything in right but I'm not sure why I get the wrong answer almost every time we do a problem in class. I am also confused as to which formula is for loans.
ReplyDelete-Jessica Nagel
Jessica, Has the review in class Monday and Friday helped with this? With the loans, you want to make sure to use the formula that has the negative exponent, with P and R.
DeleteIt was interesting to learn about being able to refinance a loan. I wasn't really aware of what refinancing completely meant previously. I think that this finance portion of the semester will be extremely helpful to be able to use in the future in real life situations. The formulas really aren't that hard, it's just a matter of learning what to plug in and where to plug it in.
ReplyDeleteI completely agree, just recently I was talking with a friend about how I have no idea what it takes to even begin thinking about buying a home. In the past two weeks, I learned how simple it is to use these formulas to help start that process! This section remains to be my favorite because of it's real life application.
DeleteHey I found the websites you showed us in class on how much your mortgage will total if you only pay what is required month to month very helpful.
ReplyDelete...mekelle
DeleteThe websites that you posted were helpful because they told you what your monthly payment would be and if is better to rent or buy a house. This chapter is going to be very helpful in the future.
ReplyDeleteAmortized Loans formula have help me keep track of what my student payments will be after college
ReplyDeleteI appreciate the the time you took to show us on the mortgage principle and the actual amount you'll pay if you only make your monthly payments on a 30 year mortgage. The zillow site was very helpful..... mekelle mcbee
ReplyDeleteThis comment has been removed by the author.
ReplyDeletethis is a unit that i will definitely be taking with me into adult life, it will be nice having the advantage of knowing how this kind of stuff works.
ReplyDeleteI never noticed how much in interest that you pay when taking out a loan or that you can end up paying more in interest than the amount of money of the loan that you borrow. It makes me scared to take out any kind of loan. But can also show that you want to have good credit so that you don't take out alone with a really high interest rate.
ReplyDelete