折现时为什么不用（1+6.5%/2）呢？

NO.PZ2024061801000032

问题如下：

A bond pays a semiannual coupon of $40 and has a current value of $1,109. The next payment on the bond is in four months, and the annual interest rate is 6.50%. Using an annual compounding assumption, the price of a six-month forward contract on this

bond is closest to:

选项：

$1,103.

$1,104.

$1,145.

$1,185.

解释：

Use the formula F = (S − I) × (1 + r)T, where I is the present value of $40 to be received in 4 months, or 0.333 years. At a discount rate of 6.50%:

I = $40 / 1.0650.333 = $39.17

F = ($1,109 − 39.17) × 1.0650.5 = $1,104.05

年化利率是6.5%，那么6个月的时间折现，折现时为什么不用（1+6.5%/2）的0.5次方呢？

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1 个答案

李坏_品职助教 · 2025年02月22日

嗨，从没放弃的小努力你好：

(1+6.5%)^0.5，这个在0.5这里已经体现出“6个月”的意思了，不需要再把6.5%除以2。这是复利计算。

如果按照单利计算的规则，可以用（1+6.5% / 2），那就不需要0.5次方。但是本题是forward contract，所以应该用复利计算。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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NO.PZ2024061801000032 问题如下 A bonpays a semiannucoupon of $40 anha current value of $1,109. The next payment on the bonis in four months, anthe annuinterest rate is 6.50%. Using annucompounng assumption, the priof a six-month forwarcontraon thisbonis closest to: A.$1,103. B.$1,104. $1,145. $1,185. Use the formula F = (S − I) × (1 + r)T, where I is the present value of $40 to receivein 4 months, or 0.333 years. a scount rate of 6.50%: I = $40 / 1.0650.333 = $39.17F = ($1,109 − 39.17) × 1.0650.5 = $1,104.05 能用画图法说明吗？谢谢按照6个月来画图，现在相当于t=2，T=6。那么40的coupon应该减去吗？

2025-02-22 16:31 1 · 回答