Questions:
A client of mine purchased a home in LA. They purchased the property for $1,000,000 with a down payment of $200,000. Their current mortgage rate is 8% with a 30-year fixed term, and the remaining principal balance is $790,000. What is their current monthly payment?

Since purchasing the home last year, mortgage rates have dropped significantly, and they’ve been offered a refinance rate of 5.625%. However, the refinancing fees would be 5.5% of the remaining principal balance. If my client decides to refinance and keep a 30-year fixed term, how long would it take them to recoup the refinancing costs through the savings on their monthly mortgage payment? Assume that the savings on principal and interest are the only factor to consider, and ignore other costs or benefits (such as tax implications or changes in property taxes).

Reference answers:
Current Mortgage Payment:
Purchase Price — $1,000,000
Down Payment — $200,000
Amount Financed — $800,000
Rate — 8.00%
Term — 360 months

Using M = P × (r(1 + r)^n) / ((1 + r)^n - 1), we can determine that the current P&I payment is $5,870.12.

To answer this question, we must determine:

1.) The current mortgage payment (answered in last question)
2.) The refinanced mortgage payment
3.) The dollar amount of the refinance costs

Refinanced Mortgage Payment:
Amount Financed — $790,000
Rate — 5.625%
Term — 360 months

Using the same formula as above, we can determine that the new P&I payment would be $4,547.69.

This new payment is $1,322.43 less than the current payment. With refinance costs of (790,000 × 5.5%) = $43,450, it would take (43,450 / 1,322.43) ≈ 33 months to break even.