Refinance Example

Mortgage rates are at their lowest since the 1950s.  It is a good time to refinance!  So my family did.

How much did we benefit?  Let's do the math...

We had a 30 year mortgage with about 23 years remaining.  As with my analysis from a week ago about whether to get a credit card that provided miles or money, I will change the dollar amounts for both the friendliness of rounded numbers and for some personal anonymity.

We'll analyze changing a $150,000 mortgage.  The original situation is a partially complete 30-year loan at 5.625%, which has a $960 monthly payment for 279 more months and then a final $184.45 payment.  The new situation is a 15-year loan at 4.5%, which has a $1,147.50 monthly payment for 179 months and then a final $45.67 payment.

The example is a bit complicated, so I included all of the details as a Google document.  If you wish, open that link in another tab or window so you can refer to it while reading the summary below.

Or, if no one has sabotaged it, here is another copy with permissions set so you can edit it: change only the cells with a colored background and all the other numbers automatically adjust!

There are two issues when refinancing.  (Well actually, there are many others, but everything else about points and fees can be wrapped up into the new loan's numbers and then ignored.)

Less Total Interest

The first real issue is how much the total interest changes.

The old loan would pay $960 per month for 279 months, and then pay $184.45.  That makes a total of $268,024.45.  Subtract the loan amount of $150,000 to get $118,024.45 of interest paid during all those 280 months.

The new loan would pay $1,147.50 per month for 179 months, and then pay $45.67.  That makes a total of $205,448.16.  Subtract the loan amount of $150,000 to get a total of $55,488.17 of paid interest.

Subtracting $118,024.45 - $55,488.17 = $62,576.28 less interest by refinancing to the new loan.

Investment Change

On the other hand, the new loan costs an extra $187.50 each month.  That money could have been put in an investment to grow with compound interest.

Now we get stuck in a subjective area: by how much would that investment grow?  I cannot predict the future of the stock market!

Let's assume that for the next 3 years the investment grows at 2%, and then from the start of year 4 onward grows at 8%.  (I'm assuming the economy will take a few years to recover and then investments will have an average rate of increase.)

On the version of the spreadsheet that you can edit you can change my assumption about how much the investment will grow.

But using my guess, we are behind $187.50 the first month, $375.31 the second month, and so on.  By the time 15 years have gone by we'll be behind $60,886.24!

Fortunately, once those 15 years are done the situation drastically improves.  Now instead of getting farther behind each month, we are done paying off the mortgage and are getting ahead by $960 each month (we are paying nothing, instead of the monthly payment of the old loan).

But compound interest still works against us.  It takes a long time to pay off a $60,886.24 debt that is earning 8% annually, compounded monthly, while only paying $960 per month.  Not until year 22 do we break even.  At the end of all 280 months we wind up only $16,750.18 ahead.

Overall

So by refinancing we end up paying $62,576.28 less interest during the next 23 years.  We also end up $16,750.18 ahead by the investment value.

The total is $62,576.28 + $16,750.18 = $79,326.46 of benefit.

In reality doing a refinance costs a few thousand dollars of fees, appraisal, insurance adjustment, and so forth.  This would come out of the cited total benefit.  But we'll still be ahead by more than $75,000.

Not bad for a few hours' hassle of phone calls and paperwork.