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.
总共那么多贷款，为什么按照3.75的利率30年还完贷款，3年后利率调成5.5之后，每月还的多了，总共还是30年还完贷款，这不逻辑矛盾了么，如果说30年还完贷款的确定的，按照3.75的利率算30期，30年能还完，3年后调整利率了，每月还的多了，怎么可能还要27年才还完？不应该提前提前还完吗？
如果说是前3年用3.75,利率，3年后调成5.5利率才能30年还完，那前3年的还款总额怎么能用30期才算呢？你用3.75利率还肯定超过30年才能还完啊。
