Pure nerdcore:
Calculating re-finance is fairly easy. Given the following:
PV = $100,000
i = 6.25% APR
n = 30 years
First, solve for payment:
100000[PV]6.25[g][12÷]30[12x][PMT] = -615.72/month
Say the homeowner wanted to re-finance after 5 years? First, clear number of periods (n) and calculate 60 months of amortization:
0[n]60[f][AMORT] = -30,280.21 (interest), and -6,662.99 (principal), found by hitting swap x/y key,
They find a loan at 5.5% over 15 years. Now we want to enter our refi data:
PV = $93.337.01 (found using [RCL][PV], but it’s already stored in the calculator, so we won’t be entering it below)
i = 5.5% APR
n = 15 years
15[g][12x]5.5[g][12÷][PMT] = -762.64/month
OMG, a higher payment! But what does that do to the remaining payments? Let’s re-amortize the remainder of the loan to figure out what the rest of this will cost us:
0[n]180[f][AMORT] = -43,938.57 (interest), and -93.336.63 (principal)
Don’t worry, you can always balloon that 38 cents, right? Look what the time value of money does here: the first five years cost the homeowner -30,280.21 in interest over the first five years., the next 15 cost only 13,707.36 more than the first 5 years in interest. Of course, it turns out that if I just double my current interest payment, I can pay off the home in 10 years (the above was a hypothetical abstraction of my current situation) for about 30/mo less than the refinance would cost with origination and other fees involved, all without modifying my savings plan. Go figure.
Of course, you could solve for n based on a monthly pre-payment, to see where an extra 200 bucks a month takes the length of the new mortgage… or you can see what paying that money to a higher interest investment does for you… or… Ahem. Best $40 bucks ever (bought it used, in perfect condition).
Also, in the above example, I’m ignoring things like closing fees, up front fees, etc that may be rolled into the refinance.