如何理解lv是3.75

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：

NZD70,424.

NZD93,899.

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.

我总觉得fv才是3.75

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1 个答案

星星_品职助教 · 2023年09月04日

同学你好，

1）借款人在当下借了5m的75%，也就是在现在这个时点从银行拿了5×75%=3.75。所以这是一个PV值（0时点的现金流）。

2）FV为结束时点的现金流。在fully amortization的规则中，每期都还本金加利息，到了结束期时正好还完所有的本息和，不会再有未还的本金剩下。所以FV或到期未还的本金是0。

简单总结一下，这3.75m是现在借的，是0时点就欠了银行3.75。不是5年后（60期后）还欠3.75m。

fully amortization中，每一期（每个月）还一部分，到了5年（60期后）正好还完了。FV=3.75相当于60时点还欠银行这么多钱。而实际是60时点还完最后一期本息和后就一分不欠了。

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