Questions:
Bob financed his home purchase with a $500,000 5/1 ARM mortgage with a 5/2/6 cap. The breakdown of his initial monthly mortgage costs is as follows:

(P&I): $2,108.62
Insurance: $250
Taxes: $500
Adjustable Rate Formula: SOFR + 3%

Bob's initial interest rate was 3%; at the time, SOFR was 2%. Today, Bob's interest rate adjusted for the first time. His new total mortgage payment is $3,638.95. Since purchasing his home, his taxes have increased to $550 a month, and his insurance premium has remained unchanged.

With this information, can we determine the current SOFR value?

After one additional year, SOFR skyrockets to 9%. Keeping in mind that Bob has a 5/1 ARM with a 5/2/6 cap—and an Adjustable Rate formula of SOFR + 3%—what can he expect Bob's new interest rate to be?

Reference answers:
Yes, this information is sufficient to determine the current SOFR value.

The first step is to determine the new P&I payment:
$3,638.95 - $250 - $550 = $2,838.95

The next step would be to determine the current interest rate on the mortgage (I). While this can't easily be solved algebraically, we can plug various values for (I) into the formula below until we arrive at an answer that is at or near $2838.95: 

Solve for I:  2838.95 = [500,000 * I * (1 + I)^360] / [(1 + I)^360 - 1]

Through trial and error, we can determine that (I) is roughly 5.5%. Furthermore, we know that the mortgage rate is now determined by SOFR + 3%:

Since we know that 5.5% = SOFR + 3%, we can say that SOFR is roughly 2.5%.

If SOFR skyrockets to 9% after one additional year, the Adjustable Rate formula of SOFR + 3% would imply that Bob's new interest rate is 12%. However, because Bob has a 5/1 ARM with a 5/2/6 cap structure, his rate increase after the initial adjustment is limited to a maximum of 2% per year. Therefore, Bob's new interest rate will be approximately 7.5%, which is his previous interest rate plus the 2%.