Consider the perpetuity that pays $3$ by the end of the 2nd year and then every $4$ years. I need to calculate the present value of it when $i=0.05$. So the second payment will be at 6th year. I thought about doing it by just discounting the first one and then express the rest of the discounts by a geometric series:
$$PV=3\cdot v^2+\sum_{k=1}^\infty 3\cdot v^{4k+2}=3\cdot \left( v^2+\frac{v^6}{1-v^4}\right)\approx15.348.$$
Is that correct?
Present value of perpetuity with one extra payment
actuarial-sciencefinance
Best Answer
Your answer is correct. However, the perpetuity formula works for the second term.
$$PV = 3v^2 + v^2\cdot \frac{3}{1.05^4-1} = 15.348$$
The second term is the perpetuity formula discounted the first two years. Saves from using the infinite sum.