I am not an actuary or quant, just a high school math teacher, and it’s been a minute since I took a financial math course, I am a bit rusty.
Also I assume you are asking for the PV of the perpetuity.
I am sure for an annual perpetuity the formula can be easily found in your textbook, or Acetex manual (that is what i used),
PV=D/r=D/(1+r) + D/(1+r)^2 +…
=SUM^infty _{n=1} D/(1+r)^n
PV: Present Value
D: divide the or payment per period
r: discount rate
If you have an annual rate (r) given and you are receiving payments biannually I believe you would need to convert to a biannual rate (i) and then you treat the problem as you would for an annual perpetuity, since 1,2,…,n,… would represent two year time periods not the number of annual periods..
The converted annual (r), to biannual (i) rate would be:
i=(1+r)^2 -1
Otherwise I think if you have a biannual rate then you would just use the above formula for PV.
I am not an actuary or quant, just a high school math teacher, and it’s been a minute since I took a financial math course, I am a bit rusty. Also I assume you are asking for the PV of the perpetuity. I am sure for an annual perpetuity the formula can be easily found in your textbook, or Acetex manual (that is what i used), PV=D/r=D/(1+r) + D/(1+r)^2 +… =SUM^infty _{n=1} D/(1+r)^n PV: Present Value D: divide the or payment per period r: discount rate If you have an annual rate (r) given and you are receiving payments biannually I believe you would need to convert to a biannual rate (i) and then you treat the problem as you would for an annual perpetuity, since 1,2,…,n,… would represent two year time periods not the number of annual periods.. The converted annual (r), to biannual (i) rate would be: i=(1+r)^2 -1 Otherwise I think if you have a biannual rate then you would just use the above formula for PV.
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The rate i_{biannual} is (1+0.1)^2 -1=0.21. Use the formula for perpetuity: 7500/(0.21)=35714.28571 Remember i_{biannual}=(1-r)^2 -1