专题一：Yield Rate 的两种情况

 此文章乃本人在section 5,6,7 & 8面对的问题做出的总结。

专题一：Yield Rate

众所周知，Yield rate就是在一个period 的overall rate.

但我发现到Yield rate的题目有两种版本。

第一）一个equation使用两个rate  （不常见）

第二）一个equation都用一样的rate. （常见）

第一版本：(一个equation使用两个rate)

Section 5a to 5c Q14

An investor pays P for an annuity which provides payments of 100 at the beginning of each months for 10 years. These payment are invested at a nominal annual interest rate of 12% compounded monthly. Monthly interest payments are reinvested at a nominal annual interest rate of 6% convertible monthly. The annual yield rate over 10 years period is 8% effective. Calculate P.

第二版本：(一个equation使用一个rate)

Section 3h Q3

On 1/1/87, Cathy borrows $1000 from ABS Finance Company and agrees to pay it back in five annual installments at an annual effective rate of 11%. The first payment is due one year after the loan is issued. On 1/1/89 Cathy pays off the balance of the loan plus a $50 prepayment penalty. Fina ABC's effective overall yield rate.

Solution : 不可以用“第一版本”来作答，不然答案一定错！

这个问题纠结了我很久，为什么同样是yield rate, 为什么有时一个equation 有两个rate, 有时只有一个rate.

经过我对于第5，6，7 和 8课的研究，我得出了一个结论！

平常题目都用第二版本(一个equation一个rate), as yield rate就是一段时间overall 的rate.

除了

看到“Reinvest" !!! 如果看到 Reinvest, 就代表已经确定用新的rate来invest了，所以只能用”第一版本“(一个equation两个rate)。

这个方法是绝对正确的✅

一般题目都是第二版本.

如果要更多第一版本的例子可以参考:

a) Section 5 (所有reinvestment rate有关yield rate题目)

b) Section 7d and 7e (Question 7) 

A 1000 20-year 8% bond with semiannual coupons is purchased for 1014, The redemption value is 1,000. The coupons are reinvested at a nominal annual rate of 6%, compounded semiannually, Determine the purchaser's annual effective yield rate over 20 year period (SOA SAMPLE/83 #5)

c) Section 8a to 8c (Question 4)

Lenny buys a stock for 200 which pays a dividend of 12 at the end of every 6 months. Lenny deposits the dividend payments into a bank account earning a nominal interest rate of 10% convertible semiannually. At the end 0f 10 years, immediately after receiving the 20th dividend payment of 12, Lenny sells the stock. The sale price assumed a nominal yield of 8% convertible semiannually and that the semiannual dividend of 12 will continue forever. Lenny's annual effective yield rate over the 10 year period is i. Calculate i. (SOA 11/93 #16)

This color = Keyword of reinvest

Conclusion: Keyword = Reinvest