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?

Answer: $35.84

Explanation:

First year

10% compounded continuously is: 10.517%

$30 X 1.10517=$33.16, then take $2 for dividend and you get ($33.16-$2) $31.16 at the end of the 1st year.

Second year

10% compounded continuously is: 10.517%

$31.16 X 1.10517-2=$32.43 at the end of 2nd year.

(-2) is the dividend for the second year to be taken out.

Third year

10% compounded continuously is: 10.517%

$32.43 X 1.10517

=$35.84

Or:

The three year forward price is gotten by deducting the PV of the returns from the current price and then grossing up to get the returns for three years at the risk-free rate.

The present value of the income is 2e-0.1*1+2e-0.1*2 = $3.447.

It is (30-3.447) e0.1*3 = $35.84