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Enjoy · 2024年10月02日

为什么不能先算出年还款额，再除以12算月的呢？

  1. CFA I
  2. Quantitative

NO.PZ2023052407000002

问题如下：

Grey Pebble Real Estate seeks a fully amortizing fixed-rate five-year mortgage loan to finance 75 percent of the purchase price of a residential building that costs NZD5 million. The annual mortgage rate is 4.8 percent. The monthly payment for this mortgage would be closest to:

选项：

A.

NZD70,424.

B.

NZD93,899.

C.

NZD71,781.

解释：

A is correct. The present value of the mortgage is NZD3.75 million

(=0.75×5,000,000), the periodic discount rate is 0.004 (=0.048/12), and the number of periods is 60 (=5×12). Using Equation 8,


Alternatively, the spreadsheet PMT function may be used with the inputs stated earlier.

B is incorrect. NZD93,899 is the result if NZD5 million is incorrectly used as the present value term.

C is incorrect. NZD71,781 is the result if the calculation is made using 4.8 percent as the rate and 5 as the number of periods, then the answer is divided by 12.

用N=5,IY=4.8,PV=3750000,FV=0,算出PMT861372,再除以12，正好等于C 选项，这样错在哪里

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1 个答案

袁园_品职助教 · 2024年10月05日

嗨，努力学习的PZer你好：


因为这种做法直接把年的PMT除以了12，没有考虑按月复利的计算方式，因此导致错误。如果按月复利的计算，需要直接使用月利率和月数来进行计算。

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