An annuity is a fixed amount that is paid once in a particular time period over an extended duration of time to the person that owns the annuity. A change in interest rate does not change the nominal amount that the investor receives. The change is in the present value of the amount that is received over the entire life of the annuity.
If the annuity is for n years and the amount paid out is P, at an interest rate of i, the present value of the annuity is P*(1 - (1+i)^n)/i).
From the formula it can be seen that an increase in the rate of interest (i) decreases the present value of the annuity whereas a decrease in the interest rate increases the present value of the annuity.