1. will be about $44.
2. will be about $ -44.
3. cannot be calculated because we aren't given the nominal interest rate.
4. cannot be calculated because we have no model of the fundamentals.
Choose the correct option.
Option 3 is the correct answer. The capital gain cannot be obtained regardless of whether the calculations are based on current dollars or on today's dollars. A current dollar calculation of the present value depends on knowing the nominal interest rate. A calculation based on today's dollars uses the real interest rate, which the question gives us, but before we make that calculation we have to adjust the $1000 and $2000 payments to put them in today's dollars. We can't make this adjustment without knowing the expected rate of inflation, which we could calculate only if we knew the nominal interest rate.
If you picked option 2 you made a correct calculation based on the assumption that the $1000 and $2000 future payments are in today's dollars. The present value of $1000 in today's dollars to be received next year will fall by $961.53 - $952.38 = $9.15 when the real interest rate rises from 4 percent to 5 percent, and the present value of $2000 in today's dollars to be received two years from now will fall by $1849.11 - $1814.06 = $35.05. The sum of $9.15 and $35.05 is $44.20. Unfortunately, the question does not state that the funds to be received are in constant dollars.
If you picked option 1 you made the same error as you would have made had you picked 2 and, in addition, got the calculations backwards---a rise in interest rates reduces the present value.
If you picked option 4 you are really confused and should go to the beginning of this topic and start again---the fundamentals are given in the question, so no model of them is necessary.