To find the breakeven month, we first need to calculate the new APR after purchasing the points. Then we can compare the total costs of the loan with points to the total costs of the loan without points. The breakeven month is the point in time at which the interest savings from buying the points equals the upfront cost of the points.
**Step 1: Calculating the new APR**
Patti is considering buying 3 points, which would reduce her APR by 0.25% per point. Therefore, the new APR can be calculated as follows:
New APR = 3.17% - (3 * 0.25%) = 3.17% - 0.75% = 2.42%
**Step 2: Comparing the total costs of the loan with points to the total costs of the loan without points**
Next, we need to calculate the total costs of the loan, both with and without points. This will allow us to determine the breakeven point.
**Loan without points:**
Given:
- Loan amount (L) = $220,000
- Interest rate (I) = 3.17%
- Loan term (T) = 30 years
Using an online mortgage calculator, we can find the total interest paid over the life of the loan.
Total interest without points = Total cost of loan - Loan amount
= $376,610.79 - $220,000
= $156,610.79
**Loan with points:**
Patti is considering buying 3 points, and each point will cost 1% of the loan value.
Total cost of points = 3 * 1% * $220,000 = $6,600
New loan amount = $220,000 - $6,600 = $213,400
Now, using the new APR and loan amount, we can calculate the new total interest paid over the life of the loan.
Total interest with 3 points = Total cost of loan with points - New loan amount
= ($366,653.03 - $213,400)
= $153,253.03
**Breakeven month calculation:**
To find the breakeven month, we compare the difference in total interest paid between the two scenarios with and without points ($156,610.79 - $153,253.03 = $3,357.76) to the upfront cost of buying the points ($6,600).
Breakeven month = Upfront cost of points / Interest savings per month
= $6,600 / ($3,357.76 / 360) (assuming loan term of 30 years)
≈ 633 months
Therefore, the breakeven point is approximately 633 months, or around 52.75 years into the loan. This means that if Patti plans to stay in the home longer than 52.75 years, purchasing the points could be beneficial in terms of overall interest cost. If she plans to stay for a shorter period than this, it may be more cost-effective to go without points.
