Final answer:
The present value of an annuity decreases when the discount rate increases, as future payments are worth less at a higher discount rate. However, increasing the number of periods per year affects the present value when considering the effects of compounding interest, potentially resulting in a different effective interest rate, which could decrease the present value.
Step-by-step explanation:
The question refers to the concept of the present value of an annuity, which is a fundamental topic in finance and mathematics. In this context, the present value (PV) of an annuity decreases when the discount rate (interest rate) increases. This occurs because each payment is discounted at a higher rate, making the present worth of each future payment smaller. However, the concept of increasing the number of periods per year does not directly relate to the present value of annuity formula. Instead, the payments frequency can impact the present value when considering the effect of compounding. If the annuity payments frequency increases but the interest is compounded at the same frequency as the payments, then there may be an increase in the effective interest rate, which could result in a lower present value, assuming compounding on a more frequent basis.
The given formula, PV = R / (1-(1+i)^-n)) captures the present value of an annuity that pays R each period at an interest rate i for n periods. If the number of periods increases but the nominal interest rate stays the same, the present value will typically decrease because payments are being discounted over a greater number of periods. However, if 'n' represents the total number of payments rather than the number of periods per year, increasing the frequency of payments (not the total number) does not imply an increase in 'n' and thus would not necessarily decrease the present value using this formula as written.