NO.PZ2022071202000014
问题如下：
Question
A borrower is considering three competing mortgage loan offers from her bank. The amount borrowed on the mortgage is $100,000 with monthly compounding.
The rate on the ARM resets at the end of Year 3. Assuming the ARM is permanently reset at 5.500% (i.e., the remaining balance on the loan is assumed to be repaid with a 5.500% stated annual interest), which of the three loans will have the smallest monthly payment after the rate reset at the end of Year 3?
选项：
A.30-year fixed-rate loan B.20-year fixed-rate loan C.30-year ARM解释：
Solution
A is correct. The timeline for the 30-year fixed rate is as follows:
where X is the monthly payment for all 360 months.
The timeline for the 20-year fixed rate is as follows:
where Y is the monthly payment for all 240 months.
The timeline for the 30-year ARM is as follows:
where Z is the monthly payment for the first 36 months (three years) and K is the monthly payment for months 37 to 360 (payment after Year 3).
The loan payments are calculated using a financial calculator.
After Year 3, the 30-year fixed-rate loan has the lowest payment: 536.82 < 559.16 < 626.46.
Note: Numbers may differ slightly from those given above because of rounding.
B is incorrect; 536.82 < 559.16 < 626.46.
C is incorrect; 536.82 < 559.16 < 626.46.
为什么ARM中的payment Z可以用30年来算？不是前三年是3.75%吗？后27年利息不同也可以直接先按3.75%来算吗？
