The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?
It's very simple: you simply multiply $30 X 1.10517=$33.16, then take $2 for dividend and you get $$31.16 at the end of the 1st.year. Then multiply this amount by 10% comp. contin. and you get
$31.16 X 1.10517 -2=$32.43 at the end of 2nd. year. Finally, you multiply this amount of $32.43 X 1.10517=$35.84 forward price at the end of 3rd.year.
This is a "hunch" solution!!!,
10% compounded contiuously is: 10.517% annual rate:
In two years the spot rate of $30, with a $ 2.00 payment should be: $32.43,
At the end of the third year the spot rate of $30.00 should be:
1.10517 X $32.43=$35.84. Well, what do you think, since you probably know the answer!!!!??.
Hey there, thanks for the answer. Well i need to solution for this question even though i got the answer. Im not sure how to write down a proper solution for this question tbh.
should i just write down the answer :
Value is 30 * e^0.10 * 3 + 2 * e^0.10 = $35.45
Is this correct?
No!. The way you have it written is not right. But do you understand what I did? I basically took your spot rate of $30 & compounded @ 10% contiuously BUT, I also considered that $ 2 dividend was paid for 2 years. Considering all that the spot rate of $30 should be worth $32.43 at the end of 2 years. And then multiply this amount by 10% compounded contiuously and you get $35.84. At any rate, I believe my calculation to be more accurate, but is NOT very far from yours. Thank you & good luck.
i got the annual compounding rate which is 1(e^0.1/1 - 1) = 10.517%
But im not sure how to calculate with the $2 payment part. Can you show the solution please.
Appreciate much
It's very simple: you simply multiply $30 X 1.10517=$33.16, then take $2 for dividend and you get $$31.16 at the end of the 1st.year. Then multiply this amount by 10% comp. contin. and you get
$31.16 X 1.10517 -2=$32.43 at the end of 2nd. year. Finally, you multiply this amount of $32.43 X 1.10517=$35.84 forward price at the end of 3rd.year.
