Chevy and Judith are purchasing a townhouse and finance $154,200 with a 30 year 5/3 ARM at 6.45% with a 4/13 cap structure what will their payments be at the beginning of the 6th year assuming they are charged maximum interest rate for that year?
a. 907.11
b. 1356.97
c. 969.58
d. 1314.26
My answer is c
To determine the monthly mortgage payments at the beginning of the 6th year, we need to follow these steps:
Step 1: Calculate the monthly interest rate by dividing the annual interest rate by 12.
Annual interest rate: 6.45%
Monthly interest rate: 6.45% / 12 = 0.5375%
Step 2: Calculate the loan balance at the beginning of the 6th year by subtracting the sum of the principal payments made in the first 5 years from the initial loan amount.
Initial loan amount: $154,200
Principal payments made in the first 5 years: (5/30) * $154,200 = $25,700
Loan balance at the beginning of the 6th year: $154,200 - $25,700 = $128,500
Step 3: Calculate the cap structure adjustment. The cap structure limits the maximum interest rate adjustment per adjustment period. In this case, the cap structure is "4/13," meaning the interest rate can be adjusted by a maximum of 4 percentage points every 13 months.
Since the 5/3 ARM has an adjustment period of 60 months (5 years), the maximum interest rate adjustment can be made every 13 months. Therefore, in 5 years, there will be 4 adjustment periods.
Maximum interest rate adjustment per period: 4 / 4 = 1 percentage point
Step 4: Calculate the maximum interest rate for the 6th year by adding the maximum interest rate adjustment to the initial interest rate.
Initial interest rate: 6.45%
Maximum interest rate adjustment: 1%
Maximum interest rate for the 6th year: 6.45% + 1% = 7.45%
Step 5: Use the loan balance and the maximum interest rate to calculate the monthly mortgage payment using the amortization formula.
Loan balance: $128,500
Monthly interest rate: 7.45% / 12 = 0.6208%
Monthly mortgage payment: $128,500 * [(0.6208%*(1 + 0.6208%)^(30*12))/((1 + 0.6208%)^(30*12)-1)] = $969.58 (approximately)
Therefore, the correct answer is option c) $969.58.