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Given that a stock is currently worth $£25$, and the forward contract delivers in $1$ year, the interest rate is $0.025$ for the first $6$ months and $0.04$ afterwards, then what is the delivery price?

I thought the answer would be $25e^{([0.025)(0.5)]}= 25.3$so this is the forward price if it was terminated here. Then for the last $6$ months $25.3e^{[(0.04)(0.5)]}.$

But apprently this method is incorrect?

the man
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  • How are you quoting interest rates? You appear to be assuming continuous compounding though that's not a standard way of quoting rates. – lulu Jun 04 '18 at 16:16
  • Yes, continuous compounding – the man Jun 04 '18 at 16:17
  • Then I don't see a problem. What makes you think the answer is incorrect? – lulu Jun 04 '18 at 16:18
  • are you sure you are meant to be using continuously compounded interest? Btw this question might be more suitable for quantitativefinance.stackexchange but users might direct you to starting references on time value of money etc. The idea i.s how much do you need to pay back in one year to borrow the 25 today to service your fward contract – Mehness Jun 04 '18 at 16:19
  • Because it’s the incorrect answer (according to my teacher). Apparently it’s $25.53$? – the man Jun 04 '18 at 16:19
  • Even if we just had a rate of $.025$ for an entire year that would be $25\times \exp (.025)\approx 25.63>25.53$. Are you sure it's meant to be a full year? – lulu Jun 04 '18 at 16:22
  • Worth remarking: even if the $.025$ represented simple interest (no compounding) then the one year forward would be $25\times (1+.025)=25.625>25.53$. – lulu Jun 04 '18 at 16:24
  • @lulu, yep initially can't see an obvious configuration of day count / period / compounding that hits the 25.53 :) – Mehness Jun 04 '18 at 16:26
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    @Mehness Yeah, I tried everything I could think of but couldn't reverse engineer the answer. – lulu Jun 04 '18 at 16:26
  • Ok, thank you for the help! – the man Jun 04 '18 at 16:30

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