Home / Money Blog

## How long to pay off?

**THE SCENARIO**
My friend Terry told me about a loan she's thinking of getting on a commercial property. She's going to be borrowing $270,000 with 30-year fully amortized financing*. The 'base' rate of the loan is 7.75%, but for 2 points (that is, 2% of the amount borrowed), she can buy the rate down to 6.75%.
**The question:** Ignoring amortization, how long will it take for Terry's lower payment to 'pay back' the points it'll take to buy down the rate of the loan?
* In actuality, though this loan amortizes over 30 years, its terms are only set for the first several years. After that, the loan becomes due or the rate begins to adjust. This is a fairly typical structure for loans on commercial buildings.

**THE SOLUTION**
This one has three parts:
**Part 1: The Base Loan**
N: 360 (The loan amortizes over 30 years)
I/YR: 7.75 (The base loan rate is 7.75%)
PV: 270,000 (Terry's borrowing $270,000)
PMT: (This is what I'm trying to find)
FV: 0 (The loan amortizes fully)
**Part 2: The Bought-down Loan**
N: 360 (The loan amortizes over 30 years)
I/YR: 6.75 (Paying 2 points drops the rate to 6.75%)
PV: 270,000 (Terry's borrowing $270,000)
PMT: (This is what I'm trying to find)
FV: 0 (The loan amortizes fully)
**Part 3: Payback Timeframe**
Terry had to pay 2 points, which is 2% x $270,000 = $5,400 to get the lower rate.
The loan with the lower rate has a monthly payment that is $1,934.31 - $1,751.21 = $183.10 less less than the Base loan.

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!

- Find the payment of the 'base' loan.
- Find the payment of the 'bought down' loan
- Find how long the monthly savings will take to repay the initial points.

The Base loan's monthly payment is **$1,934.31**.

The monthly payment is **$1,751.21** if Terry buys down the rate.

Therefore, if Terry pays the points to lower the rate, it'll take her $5,400 / $183.10 = **29.49 months** (about 2 ½ years) to break even.

What would you do in Terry's situation? Would you buy down the rate, or save your $5,400? Would the answer to the question change if you were planning to hold the building long-term versus offloading it quickly? Let us know in the comments!