Refinancing and Paying Ahead

Last week, we saw two ways to save money in an amortized loan.  The first option was to refinance. This means to transfer the outstanding balance of your loan to a newer loan with a lower interest rate (and perhaps a different term).  To do this, you must find the unpaid balance of your loan.  The formula for this looks just like the formula we use for an amortized loan with P replaced by U and the mt in the exponent replaced with N, where N is the number of payments remaining on the loan:
 \[ U = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-N}}{\frac{r}{m}}\right] \]

The second way to save we looked at was to pay extra towards reducing your principal each month.  We called this "paying ahead".  In this situation, we want to use the formula for the amortized loan to solve for t to determine how soon we would pay off the loan.  You should also be able to determine how much money you save by paying a fixed amount extra each month.
 \[ P = R\left[\dfrac{1-\left(1+\frac{r}{m}\right)^{-mt}}{\frac{r}{m}}\right] \]

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 Tuesday, April 10) 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.