jeduhi wrote:
I would very much appreciate if you would provide me with all relevant equations. I'm a number cruncher. I want to pay the least amount possible (obviously) and we do have some equity in the house. I guess a lot will have to do with what the bank appraises the house at.AMEX statement cuts on the10th so looking to move quickly after a decision is made and start the refinance process.
It's simple enough. The formula for calculating a monthly payment is:
Monthly Payment = [L(r/12)(1+r/12)^t] / [({1+r/12}^t)-1]
Where:
L = Loan amount (in dollars)
r = annual interest rate (in decimal form, e.g., 4% = 0.04)
t = lifetime of loan (in months, e.g., 30 years = 360 months)
(Note: the rich text editor used in the MyFICO forums doesn't allow exponents, so the caret sign (^) implies an exponent, just in case you weren't familiar with that notation.)
As an example, let's say you purchased a home eight years ago for $300,000. You put $50,000 down, and hence, had to get a mortgage to cover the other $250,000. Let's further assume you were given an interest rate of 6.007% (i.e., 0.06007). Your monthly payment on this loan (principle and interest only; does not include PMI, property tax, or home owner's insurance) would be:
Monthly Payment = [$250,000(0.06007/12)(1+0.06007/12)^360]/[({1+0.06007/12}^360)-1] = $1,500.00 per month
The total repayment for this loan would simply be the monthly payment ($1,500.00 per month) times the lifetime of the loan (360 months), or $540,000, which is 2.16 times the original loan amount ($250,000). At the end of any given month, the remaining principle on the loan is simply the principle amount from the previous month plus whatever interest has accrued during that month. This is because the interest accrued in a mortgage is compounded monthly, not annually, which is why the annual interest rate (r) in the aforementioned formula is always divided by 12. The amount of interest accrued is simply:
Interest Accrued = (P)(r/12)
Where:
P = the remaining principle from the previous month (in dollars)
r = annual interest rate (in decimal form)
So for example, at the end of the first month of the life of the loan, the accrued interest would be:
Interest Accrued = ($250,000)(0.06007/12) = $1,251.46
As a consequence, the actual balance on the mortgage at the end of the first month is $251,251.46. When you send in your first mortgage payment of $1,500, the remaining mortgage balance becomes $249,751.46. At the end of the second month, another $1,250.21 in interest accrues, resulting in a remaining balance of $251,001.67. When you send in your second mortgage payment, this decreases to $249,501.67. You can see that the amount of interest that accrues each month will decrease each time you make a payment, since the remaining balance gets incrementally smaller and smaller.
Now, after paying $1,500.00 per month for eight years (96 months), the remaining balance on the mortgage account (including principle and interest) will be $219,462.70 (to get this number, we simply need to carry forward the aforementioned interest calculations for 96 months, which is relatively easy to do if you're familiar with making an Excel spreadsheet; online calculators can do the same). If after those eight years you decided to refinance, that would be the minimum amount you'd need to refinance. I say "minimum" because let's recall you could also roll the fees for refinancing (if any) into the new loan amount, thereby increasing the actual amount you'd need to borrow. To keep things simple, however, let's just assume you paid the fees upfront with cash and only had to refinance the remaining balance on the mortgage, but at a lower interest rate (since, after all, a lower interest rate is the only reason you'd want to refinance). Let's look at a couple scenarios: 1) a new 30-year mortgage at 4.25%; and 2) a 15-year mortgage at 3.75%. Here's how the numbers work out:
Scenario 1: Monthly Payment = [$219,751.46(0.0425/12)(1+0.0425/12)^360]/[({1+0.0425/12}^360)-1] = $1,081.05 per month
Scenario 1: Total Repayment = ($1,081.05 per month)(360 months) = $389,178.00
Scenario 2: Monthly Payment = [$219,751.46(0.0375/12)(1+0.0375/12)^180]/[({1+0.0375/12}^180)-1] = $1,595.98 per month
Scenario 2: Total Repayment = ($1,595.98 per month)(180 months) = $287,276.40
Obviously, the first scenario offers considerably lower monthly payments, but a much higher total repayment due to the higher interest rate and the longer lifetime of the loan. By contrast, the second scenario offers a monthly payment that's fairly close to what you're currently paying, but with much greater savings in the life of the loan. Which option you choose is going to depend on what is more important to you, i.e., having a lower monthly payment (in order to afford other expenses) or being able to save money (over $100K in this example) in the long run.
Once you have all of that data, it's important to consider if refinancing is even right for you given what the numbers say. For example, recall that we calculated the total repayment of the original mortgage would be $540,000. Given that after 96 months the owner has paid back $144,000, the total repayment remaining would be $396,000. You'll notice that the refinance in Scenario 1 shows a total repayment of $389,000, which is very close to how much was already left on the original loan. After you consider all the fees and time that would be required to refinance, refinancing may not turn out to be worth your time, money, and effort. For a refinancing scenario to be worth it, it has to offer savings that make the time and effort worth it. In this case, the refinance in Scenario 2 makes much more sense, provided you can afford the slightly higher monthly payment, since it will save you about $109,000 over the original mortgage. This is precisely why you need to run the numbers for a refinance first before you dive headlong into one -- it may turn out that it's either simply not worth it (as in Scenario 1) or too expensive on a monthly basis (as in Scenario 2).
I hope that helps.
