Home / Money Blog

## How Long To Hold?

Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!
Image Source
THE SCENARIO In the past, we've covered the concept of paying money up-front when getting a loan in order to get a lower interest rate. This week, I was evaluating just such a situation, and determined that I could make a 17.65% return on my money if I bought the rate down as much as the lender will allow. However, I only achieved that return if I kept the loan until it was entirely paid off, and oftentimes loans are paid off through sale or refinance before their entire (usually 30-year) term elapses. The question: If I want to make at least 10% on my up-front rate-buydown money, how long will I have to keep the loan*? Ignore amortization, and concentrate only on month-to-month cash flow with no future payoff. * The loan they offered me has a balance of \$83,500 at 6.875% for 30 years, fully amortizing (we'll call it the "base" loan), but if I pay \$5,035, I can reduce the interest rate to 5.5% (we'll call it the "bought-down" loan).
THE SOLUTION This one has several parts, but they're all pretty straightforward.
1. Find out the payment on the 'base' loan.
2. Find out the payment on the 'bought-down' loan.
3. Find out the monthly savings by buying down the rate.
4. Find out how long I'd have to keep the bought-down loan to make 10% on my \$5,035.
First things first, make sure the calculator is using 12 Payments per Year. Step 1: The Base Loan N: 360 (This is a 30-year loan, which is 30 x 12 = 360 months) I/YR: 6.875 (The 'base' loan rate is 6.875%) PV: 83,500 (The original borrowed amount is \$83,500) PMT: (This is what I'm trying to find) FV: 0 (The loan amortizes fully)

The payment on the 'base' loan is \$548.54.

Step 2: The Bought-Down Loan N: 360 (This is a 30-year loan, which is 30 x 12 = 360 months) I/YR: 5.5 (The rate can be bought down to 5.5%) PV: 83,500 (The original borrowed amount is \$83,500) PMT: (This is what I'm trying to find) FV: 0 (The loan amortizes fully)

The payment on the 'bought-down' loan is \$474.10.

Step 3: Monthly Savings The payment on the 'base' loan is \$548.54, and on the 'bought-down' loan is \$474.10. The monthly savings from buying down the loan is \$548.54 - \$474.10 = \$74.44. Step 4: How Long To Keep It? N: (This is what I'm trying to find) I/YR: 10 (My target return is 10%) PV: -5,035 (It cost me \$5,035 to buy down the rate) PMT: 74.44 (This is my monthly savings from buying down the rate) FV: 0 (At the end, no money changes hands)

To make 10% on my buydown money, I'd have to keep the loan for 99.94 months (around 8 years and 4 months).

Given that the buydown doesn't break even until \$5,035 ÷ \$74.44 = 67.74 months into the loan, this result isn't very surprising.

What would you do? Would you buy down the rate, locking in a lower monthly payment? Or would you keep the higher rate, and keep your eye out for a profitable sale opportunity in the nearer term? What factors would lead you to do one versus the other? Let us know in the comments!