Final answer:
The present value of an annuity will be lowest with a higher interest rate, since future payments are more heavily discounted as interest rates increase.
Step-by-step explanation:
When holding constant the annuity amount, number of periods, and interest rate, the option that will have the lowest present value is Option 1: A higher interest rate. Using the formula provided, the present value (PV) of an annuity is inversely related to the interest rate (i), meaning as the interest rate increases, the present value decreases. This is because the future payments are discounted more heavily at a higher interest rate. Conversely, if the interest rate decreases, each future payment is discounted less, resulting in a higher present value.
It's important to note that the other options, such as a longer number of periods or a lower annuity amount, also impact the present value, but they are not relevant to the question since the annuity amount and number of periods are held constant. Therefore, when comparing present values with different interest rates, the one with the higher interest rate will result in the lowest present value for the annuity.